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Friday, 02 September 2011 09:52

# Seminar on Orthogonality, Approximation Theory and Applications

Contact:

Thursday, June 14 2012, 16:00. Room 2.2.D08

Speaker: Carl Jagels, Hanover College (USA).

Title: The Laurent-Arnoldi Process.

Abstract: The Laurent-Arnoldi process is an analog of the standard Arnoldi process applied to the extended Krylov subspace. It produces an orthogonal basis for the subspace along with a generalized Hessenberg matrix whose entries consist of the recursion coefficients. As in the standard case, the application of the process to certain types of linear operators results in recursion formulas with few terms. One instance of this occurs when the operator is isometric. In this case, the recursion matrix is the pentadiagonal CMV matrix and the Laurent-Arnoldi process essentially reduces to the isometric Arnoldi process in which the underlying measures differ only by a rotation in the complex plane. The other instance occurs when the operator is Hermitian. This case produces an analog of the Lanczos process where, analogous to the CMV matrix, the recursion matrix is pentadiagonal. The Laurent polynomials generated by the recursion coefficients have properties similar to those of the Lanczos polynomials. We discuss the interpolating properties of these polynomials in order to determine remainder terms for rational Gauss and Radau rules. We then apply our results to the approximation of matrix functions and functionals.

Thursday, June 7 2012, 16:00. Room 2.2.D08

Speaker: Rubén Vigara Benito, Centro Universitario de la Defensa de Zaragoza

Title: Representación de 3-variedades por esferas de Dehn rellenantes.

Abstract: Una esfera de Dehn rellenante S en una 3-variedad (compacta y conexa) M es una 2-esfera inmersa en M que produce una descomposición celular de M. La preimagen en la 2-esfera de las singularidades de S forman un diagrama a partir del cual es posible reconstruir M. Estas esferas y sus diagramas representan, por tanto, a las 3-variedades donde viven. En el año 2000, J.M. Montesinos demostró que toda 3-variedad contiene esferas de Dehn rellenantes. Presentaremos este resultado junto con otros que han sido obtenidos desde entonces, así como diversos problemas abiertos.

Thursday, May 31 2012, 16:00. Room 2.2.D08

Title: Caracterización de la hiperbolicidad en grafos planos periódicos.

Abstract: Daremos en primer lugar una visión general de los resultados sobre hiperbolicidad de grafos desarrollados en los últimos años, tanto desde el punto de vista teórico como de las aplicaciones. A continuación abordaremos uno de los problemas abiertos más importantes de la teoría: caracterizar, de forma sencilla, los grafos que son hiperbólicos. Debido a la complejidad del problema, resulta natural estudiarlo para una subclase de grafos, donde el problema es más asequible: esta clase es la de los grafos planos periódicos.

Thursday, May 24 2012, 16:00. Room 2.2.D08

Speaker: Óscar Ciaurri, Universidad de La Rioja.

Title: Acotaciones con pesos para series de Fourier: una perspectiva familiar.

Abstract: A mediados de los años ochenta del siglo pasado, José Luis Rubio de Francia propuso a J. J. Guadalupe estudiar acotaciones con pesos de los operadores de suma parcial para series de Fourier de polinomios ortogonales usando la teoría de pesos Ap. Ese fue el inicio de la línea de investigación principal que hemos desarrollado en nuestro grupo. El objeto de esta charla es presentar algunos de los distintos resultados que hemos ido obteniendo y mostrar las nuevas líneas de trabajo de nuestro grupo.

Thursday, May 17 2012, 16:00. Room 2.2.D08

Title: Some properties and applications of orthogonal polynomials in the complex plane.

Abstract: We consider analytical and computational properties of polynomials that are orthogonal on certain contours in the complex plane. The study of these orthogonal polynomials and the distribution of their zeros is important in the design of complex Gaussian quadrature rules, and also in the analysis of the partition function and free energy of certain random matrix ensembles. As a particular case, we mention the unitary random matrix model with weight function $e^{-NV(z)}$, where $V(z)=z^2/2-uz^3$ and $u>0$ is a real parameter. This is joint and ongoing work with Pavel M. Bleher, (Indiana University-Purdue University Indianapolis, USA), Daan Huybrechs and Arno B. J. Kuijlaars (K.U. Leuven, Belgium).

Thursday, May 10 2012, 16:00. Room 2.2.D08

Title: La matriz de Hessenberg correspondiente a polinomios ortogonales sobre curvas y la aplicación de Riemann.

Abstract: Estudiamos el comportamiento --asintóticamente Toeplitz-- de la matriz de Hessenberg cuando partimos de medidas que satisfacen la condición de Szego sobre curvas de Jordan analiticas, obteniendo el límite de las diagonales de dicha matriz.

Thursday, May 3 2012, 16:00. Room 2.2.D08

Title: Núcleos reproductores en espacios de Banach.

Abstract: Estudiaremos cómo los núcleos reproductores en espacios de Hilbert proporcionan una buena solución para varios problemas básicos en algoritmos de aprendizaje. Sin embargo, para otros problemas necesitamos normas no hilbertianas. Por ello, desarrollamos la idea de núcleos reproductores en espacios de Banach sin el requerimiento de la existencia de productos internos ni semi-internos. Finalizaremos aplicando esta construcción al problema de máquinas de soporte vectorial.

Thursday, April 26 2012, 16:00. Room 2.2.D08

Speaker: Andrei Martínez-Finkelshtein, Universidad de Almería.

Title: Problemas de max-min de energía y simetría de la medida de equilibrio.

Abstract: Los problemas extremales de la teoría de potencial juegan un papel relevante en varias ramas de las matemáticas (teoría de aproximación, polinomios ortogonales, matrices aleatorias, cuadraturas complejas, sistemas integrables, etcétera). Entre ellas tienen una importancia especial aquellos cuya solución presenta una cierta propiedad de simetría ("propiedad S"), ya que las medidas correspondientes describen, por ejemplo, la distribución asintótica de ceros de familias de polinomios de ortogonalidad no-hermitiana.
En esta charla voy a introducir el concepto de medidas críticas
(puntos estacionarios de un funcional de energía) y demostrar que dichas medidas poseen la propiedad de simetría antes indicada.

Thursday, April 19 2012, 16:00. Room 2.2.D08

Title: Gaussian quadrature rules connect Fourier series.

Abstract: Sequences of orthogonal polynomials of a wide class of varying measures are considered. A connection between their Fourier series and Gauss quadrature formulae is found. Such connection allows to prove conditions of convergence for both constructions.

Thursday, April 12 2012, 16:00. Room 2.2.D08

Speaker: María Jesús Carro, Universidad de Barcelona.

Title: Teoremas de Boyd y Lorentz-Shimogaki en espacios de Lorentz con pesos.

Abstract: Los teoremas clásicos de Lorentz-Shimogaki y Boyd hacen referencia a espacios invariantes por reordenadas y caracterizan respectivamente cuando el operador maximal o el operador transformada de Hilbert son acotados en X en función de los llamados índices de Boyd.

En esta charla extenderemos estos teoremas  a los espacios de Lorentz con pesos, los cuales incluyen como caso particular los espacios de Lebesgue con pesos. Estos espacios no son r.i. por lo que una nueva definición de índices de Boyd para estos espacios ha de ser dada.

Thursday, March 22 2012, 16:00. Room 2.2.D08

Title: Some results about large solutions for nonlinear elliptic equations and their applications.

Abstract: In this talk I discuss results related to large solutions for elliptic equations with nonlinear lower order terms. I explain the main difficulties in approaching this kind of problem (existence, uniqueness, asymptotic behavior) and I fix the attention on a class of quasilinear equations. I present some results obtained in collaboration with A. Porretta concerning the expansion of the gradient near the boundary and I discuss their application to a stochastic control problem with state constraint.

Thursday, March 15 2012, 16:00. Room 2.2.D08

Speaker: Jeff Geronimo, Georgia Institute of Technology (Chair of Excellence Santander-UC3M 2011).

Title: Some problems associated with two variable polynomials orthogonal on the bi-circle

Abstract: I will go into more depth on a couple of topics mentioned in my Colloquium two weeks ago. In particular I will discuss the connection between Matrix orthogonal polynomials on the unit circle and two variable polynomials orthogonal on the bi-circle. I will also mention some open problems.

Thursday, March 8 2012, 16:00. Room 2.2.D08

Speaker: Anbhu Swaminathan, Indian Institute of Technology Roorkee.

Title: Pick functions, chain sequences and hypergeometric type functions.

Abstract: Pick functions were studied by Nevanlinna using moment problems as reciprocal of Stieltjes functions. They are useful in finding solutions of certain differential difference equations. Using chain sequences or q-fractions, ratios of certain hypergeometric type functions can be obtained as members of the class of Pick functions. The chain sequences of infinite and finite classical orthogonal polynomials are useful in determining certain interesting properties. n this lecture we will survey the  interplay between techniques on orthogonal polynomials and linear algebra with an special emphasis on the inversion of Hankel and Toeplitz matrices, factorization of some structured matrices, eigenvalue problems, least square problems, and functions of matrices. Some applications in digital filter structures will be shown.

Thursday, March 1 2012, 16:00. Room 2.2.D08

Speaker: Francisco Marcellán Español, Universidad Carlos III

Title: Matrix Analysis meets Orthogonal Polynomials

Abstract: In this lecture we will survey the  interplay between techniques on orthogonal polynomials and linear algebra with an special emphasis on the inversion of Hankel and Toeplitz matrices, factorization of some structured matrices, eigenvalue problems, least square problems, and functions of matrices. Some applications in digital filter structures will be shown.

Thursday, February 23, 2012. 4:00 pm. Room 2.2.D08

Title: Convergence of simultaneous Fourier-Padé approximation.

Abstract: We give a Montessus type theorem for row sequences of simultaneous Fourier-Pad\'e approximations of a finite system of functions which are analytic on a neighborhood on the closed unit disk. The aim is to recover the functions in the largest possible domain and detect the location and order of their poles in terms of the convergence properties of the approximating rational functions.

Thursday, February 16, 2012. 4:00 pm. Room 2.2.D08

Speaker: Renato Álvarez-Nodarse, Universidad de Sevilla

Title: On the properties of some tridiagonal $k$-Toeplitz matrices

Abstract: Motivated by a physical model of a system of quantum oscillators with nonlinear interactions, we study spectral properties of certain matrices which arise as perturbations of some tridiagonal $k-$Toeplitz matrices. Concretely, we are interested in the spectral properties of general tridiagonal $k-$Toeplitz matrices (which are $k-$periodic Jacobi matrices) and certain perturbations of them. We will show in this talk how the theory of orthogonal polynomials (and in particular the polynomial mappings) can be used for solving the unperturbed case. For the perturbed case we will focus our attention on the localization of the eigenvalues of such matrices, as well as on the distance between two consecutive eigenvalues.

Thursday, February 9, 2012. 4:00 pm. Room 2.2.D08

Title: Esquemas de subdivisión y de multirresolución no lineales. Estudio de la estabilidad

Abstract: En esta charla vamos a presentar algunos operadores de reconstrucción no lineales ( ENO (Essentially Non Oscillatory), ENO con resolución subcelda, WENO (Weighted ENO), PPH (Piecewise Polynomial Harmonic).

Utilizaremos dichos operadores de reconstrucción dentro de los esquemas de subdivisión y de multirresolución de Harten. Comentaremos las dificultades que aparecen para probar la estabilidad de los algoritmos al tratar con la no linealidad de estos operadores de reconstrucción. Introduciremos también los algoritmos con control del error, que suponen una alternativa para estabilizar los esquemas no lineales inestables.

Entre las aplicaciones de esta teoría se pueden citar la compresión y el zoom de datos, la eliminación de ruido en señales, la integración numérica y la reducción del tiempo computacional de ciertos algoritmos numéricos como el cálculo de flujos en ecuaciones hiperbólicas.

Thursday, February 2, 2012. 4:00 pm. Room 2.2.D08

Speaker: Kenier Castillo, UC3M

Title: Szegö and para-orthogonal polynomials on the real line

Abstract: We study polynomials which satisfy the same recurrence relation as the Szegö polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-ortogonal polynomials that follows from these Szegö polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szegö polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szegö polynomials and polynomials arising from canonical spectral transformations are obtained.

Thursday, January 19, 2012. 4:00 pm. Room 2.2.D08

Speaker: Jorge Bosch, Centro de Neurociencias de Cuba (CNEURO)

Title: Social Brain Interaction: de los primeros modelos a series temporales

Abstract:  Para las Neurociencias en la actualidad las neuroimágenes no constituyen la única fuente valiosa de información. El estudio de ciertas variables biológicas y aspectos de la conducta están ofreciendo información relevante para extraer conclusiones acerca del funcionamiento del cerebro. Un área emergente es el estudio del cerebro en sus interacciones sociales: los movimientos de los ojos, la cabeza, diferentes músculos o partes del cuerpo, pueden implicar intenciones en la comunicación u ofrecer patrones de la conducta humana. Caracterizar dichos patrones puede ayudar a identificar patrones patológicos que contribuyan al diagnóstico de enfermedades. Un ejemplo es el autismo.

Este mismo objetivo, en el plano social consiste en determinar las relaciones de causalidad que ocurren entre dos o más personas en una situación de interacción social: cómo evolucionan los procesos de atención y liderazgo, que pueden condicionar determinados patrones de comportamiento.

El análisis del cerebro evoluciona al estudio simultáneo de dos o más cerebros que interactúan socialmente. Una pregunta importante a responder es cómo la activación de ciertas áreas en una persona puede estar condicionada, o puede condicionar, la activación de otras áreas en el cerebro del compañero.
El ya grave problema de la alta dimensionalidad de las neuroimágenes (varias decenas de miles de variables, en algunas ocasiones con una pobre resolución temporal, como es el caso de la fMRI), se duplica al estudiar dos cerebros, a la vez que se trata de combinar diferentes modalidades de datos.

En esta presentación resumimos algunos de nuestros intentos por dar respuesta a algunos de estos problemas. Para ello aplicamos métodos de análisis de series temporales al estudio de diferentes modalidades de información procedentes tanto del cerebro como de variables biológicas relacionadas, como movimientos de los ojos, la cabeza y otros músculos.

Thursday, January 12, 2012. 4:15 pm. Room 2.2.D08

Speaker: Abey López García, Katholieke Universiteit Leuven (Belgium)

Title: Multiple orthogonal polynomials and the normal matrix model.

Abstract: The normal matrix model is a certain probability measure defined on the space of complex matrices, introduced by phisicists P. Wiegmann and A. Zabrodin. This model is not well-defined for arbitrary polynomial potentials. In order to resolve this theoretical obstacle P. Elbau and G. Felder proposed the so-called cut-off approach, which consists of restricting the model to those matrices with eigenvalues contained in a fixed compact subset of the complex plane. The orthogonal polynomials that are relevant to the study of the cut-off model possess many interesting properties, probably the most remarkable being that they satisfy an almost three-term recurrence relation, and that for some potentials the zeros of these polynomials accumulate on a star-like set. Recently, P. Bleher and A. Kuijlaars proposed a new approach to the normal matrix model, which introduces certain unbounded contours and leads naturally to the study of multiple orthogonal polynomials associated to varying exponential weights defined on these contours. Bleher and Kuijlaars conjectured that the zeros of these multiple orthogonal polynomials have the same asymptotic distribution as the zeros of the orthogonal polynomials in the cut-off approach of Elbau and Felder. This was shown to be true in the case of a cubic monomial potential by Bleher and Kuijlaars. In this talk we discuss the case of a quartic monomial potential. Our main tool is the application of the Riemann-Hilbert asymptotic analysis to the multiple orthogonal polynomials. This is a joint work in progress with A. Kuijlaars.

Thursday, December 15, 2011. 4:15 pm. Room 2.2.D08

Speaker: Kurusch Ebrahimi-Fard, CSIC-UAM-UC3M-UCM

Title: B-series from an algebraic and combinatorial point of view?

Abstract: Numerical integration methods are used for calculating numerical solutions of differential equations. Since the work of John Butcher on an algebraic theory of integration methods, in the late 1960s - early 1970s, so-called Butcher- or B-series provide important tools in the analytic and structural study of -particular classes of- such numerical methods. Concerning applications in numerical analysis, one of the natural things to do with such B-series is to combine them. Indeed, a composition law for B-series for example allows for a simple derivation of order conditions. A substitution law for B-series makes the notion of modified differential equations in the context of backward error analysis more transparent. These two laws give rise to algebraic structures, such as groups, and (pre-)Lie and Hopf algebras of trees. In this talk we will first introduce Butcher's work and review related structures, in particular, Lie and Hopf algebraic ones. Once the basic notion of B-series has been outlined, we will introduce a new Hopf algebra of rooted forests, and show how it relates to substitution of B-series. We establish a link between this Hopf algebra and the well-known Butcher-Connes-Kreimer Hopf algebra of rooted trees, which will allow us to link it to Butcher's original work on composition of B-series. We will show how these results enable us to recover recent results in the field of numerical methods for differential equations due to Chartier, Hairer and Vilmart as well as Murua.

Reference: D. Calaque, KEF and D. Manchon, "Two interacting Hopf algebras of trees",  Advances in Applied Mathematics, 47, (2011) 282-308.

Thursday, December 1, 2011. 4:15 pm. Room 2.2.D08

Speaker: Miguel Antonio Jiménez Pozo, Benemérita Universidad Autónoma de Puebla (Mexico) and Universidad de Jaén (Spain).

Title:  Asymmetric approximation.

Abstract: In this talk we introduce the usual subjects of approximation theory in the case when distances in use are not necessarily symmetric. This means that d(x,y) could be different of d(y,x). Related to an asymmetric sup distance this type of approximation was initiated by Moursund in the 60’s with the use of a generalized weight function. By this time Krein and Nudelmann used the incipient concept of asymmetric norm to study approximation problems and moment problems as well. A later development by the Russian and Ukrainian schools converged to the so called sign sensitive approximation and still more general approximation by positive homogeneous functionals. A third way of measuring the asymmetric approximation in connection with the sup norm was introduced by the speaker in dealing with mathematical models in industry. Each of these ways has its particular interest but it happens at the end all of them are equivalent. Krein and Nudelmann also replaced the sup asymmetric norm by an integral one. At present asymmetric integral approximation is another active subject of mathematical research that shall be briefly focused in this talk.

Thursday, November 24, 2011. 4:15 pm. Room 2.2.D08

Speaker: Maxim Derevyagin, TU Berlin

Title: A tridiagonal approach to interpolation problems.

Abstract: We will discuss how to generalize the fruitful interaction between Jacobi matrices, orthogonal polynomials and Padé approximation to the case of rational interpolation (i.e. the multipoint Pade approximation for a Newton table). Actually, it will be demonstrated that in order to do so it is natural to consider linear pencils H-zJ of tridiagonal matrices H and J, (bi)orthogonal rational functions and rational interpolants (multipoint Padé approximants). In fact, this approach enables us to prove some convergence results for rational interpolants. Also, the approach gives an idea on how to introduce some generalizations of Darboux transformations related to biorthogonal rational functions.

Thursday, November 17, 2011. 4:15 pm. Room 2.2.D08

Title: Some information-theoretic properties of orthogonal polynomials

Abstract: The spreading of the classical orthogonal polynomials p_n(x) is investigated by means of several theoretic measures of the associated Rakhmanov probability densities, \rho_n(x) = w(x)p_n(x)^2, where w(x) is the corresponding weight function. These information measures range from the well known standard deviation, Shannon and Rényi entropies or Fisher information, to the associated spreading lengths or the composite complexity measures. These quantities and their asymptotic behaviours are obtained by different methods and techniques. The evaluation of the Rényi entropy, which is closely related to the Lq norm of the polynomials, is highlighted in this talk since it is calculated by use of some scarcely known linearization formulas of various types which make use of generalized multivariate hypergeometric functions. Finally, the asymptotics of the L^q norms of Hermite polynomials will be discussed.

Thursday, November 10, 2011. 4:15 pm. Room 2.2.D08

Speaker: Galina Filipuk, Warsaw University (Poland)

Title: Semi-classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) and the Painlevé equations.

Abstract: In this talk I shall present recent results on semi-classical discrete orthogonal polynomials and explain connection to the third and fifth Painleve equations. This is a joint work with W. Van Assche, L. Zhang, L. Boelen and C. Smet (KULeuven).

Thursday, November 3, 2011. 4:15 pm. Room 2.2.D08

Speaker: Pablo Manuel Román, Katholieke Universiteit Leuven (Belgium)

Title: Vector equilibrium problems arising from a model of non-intersecting squared Bessel paths

Abstract: In this talk I will consider a model of n non-intersecting squared Bessel processes with parameter \alpha, in the confluent case where all particles start, at time t = 0, at the same positive value x = a, remain positive, and end, at time T = t , at the position x = 0 or at a positive value x=b. I will discuss how the limiting mean density of the positions of the paths, as n tends to infinity, can be characterized by a vector equilibrium problem, which involves two measures if the particles end at x=0 and involves three measures when the particles end at a nonzero value x=b.

Thursday, October 27, 2011. 4:15 pm. Room 2.2.D08

Speaker: Ulises Fidalgo Prieto, UC3M

Title: A generalization of Markov's Theorem.

Abstract: A wide class of systems of Markov's functions supported on the same interval called Nikishin systems of functions are considered. A very general sufficient conditions to have uniform convergence for sequence of type II Hermite-Padé approximations corresponding to such systems of functions are given.

Thursday, October 20, 2011. 4:15 pm. Room 2.2.D08

Speaker: Marta Llorente, UAM, Spain

Title: Un algoritmo para el cálculo de medidas fractales

Abstract: Un tema central en el desarrollo de la teoría sobre conjuntos fractales es el cómputo exacto de su medida. Sin embargo en la práctica es muy difícil calcular el valor exacto de las medidas fractales. En los últimos años los investigadores se han aproximado a este problema considerando conjuntos concretos en los que el cálculo de las medidas fractales es posible. Recientemente hemos desarrollado un algoritmo que permite el cálculo de la medida centrada de Hausdorff para una amplia clase de conjuntos autosimilares que engloba todos los conjuntos previamente estudiados en la literatura. En la charla, combinaré resultados teóricos sobre la naturaleza del algoritmo con ejemplos concretos que muestran su efectividad. Todo el programa es un trabajo conjunto con Manuel Moran de la Universidad Complutense de Madrid.

Thursday, October 13, 2011. 4:15 pm. Room 2.2.D08

Speaker: Sergio Medina Peralta, UC3M, Spain

Title: Sobre la perfección de sistemas AT-Nikishin mixtos.

Abstract: Estudiamos los aproximantes Hermite-Padé de tipo mixto para una clase amplia de funciones analiticas. Entre los resultados expuestos, responderemos a la cuestión de la unicidad de los aproximantes Hermite-Padé de tipo mixto y la perfeccción de los sistemas de funciones analizadas.

Thursday, October 6, 2011. 4:15 pm. Room 2.2.D08

Speaker: Pedro Tradacete Pérez, UC3M, Spain

Title: Teoría de extrapolación en espacios Lp-débiles.

Abstract: Resolvemos el problema de extrapolación para operadores en $L^{p, \infty}(\mu)$; es decir, proporcionamos estimaciones extremales (cuando p tiende a 1) para operadores sublineales T tales que $T:L^{p,\infty}(\mu)\rightarrow L^{p, \infty}(\nu)$ es acotado con constante menor o igual que $1/(p-1)^m$. Presentamos también algunas aplicaciones para el operador maximal de Hardy-Littlewood, la transformada de Hilbert y composición de operadores. Es un trabajo conjunto con María J. Carro.

Thursday, September 29, 2011. 4:15 pm. Room 2.2.D08

Speaker: Héctor Raúl Fernández Morales, UC3M, Spain

Title: Generalized sampling in $L^2(R^d)$ shift-invariant subspaces with multiple stable generators

Abstract: In order to avoid most of the problems associated with classical Shannon's sampling theory, nowadays signals are assumed to belong to some shift-invariant subspace. In this work we consider a general shift-invariant space $V_\Phi^2$ of $L^2(R^d)$ with a set $\Phi$ of $r$ stable generators. Besides, in many common situations the available data of a signal are samples of some filtered versions of the signal itself taken at a sub-lattice of $Z^d$. This leads to the problem of generalized sampling in shift-invariant spaces. Assuming that the $\ell^2$-norm of the generalized samples of  any $f\in V_\Phi^2$  is stable with respect to the $L^2(R^d)$-norm of the signal $f$,  we derive frame expansions in the shift-invariant subspace allowing the recovery of the signals in $V_\Phi^2$ from the available data. The mathematical  technique used here mimics the Fourier duality technique which works for classical Paley-Wiener spaces. Irregular samples are also obtained as a perturbation of the regular ones, the irregular sampling results arise from the theory of perturbation of frames, finally a frame algorithm is implemented in the $\ell^_r(Z^d)$ setting.

Thursday, September 22, 2011. 4:15 pm. Room 2.2.D08

Speaker: Junot Cacoq, UC3M, Spain

Title: Some results on the convergence of rows of simultaneous Padé approximation

Abstract: In this talk we present results on the convergence of rows of simultaneous Padé approximation which extend previous ones of P.R. Graves-Morris and E.B. Saff.

Thursday, September 15, 2011. 4:15 pm. Room 2.2.D08

Speaker: Edmundo Huertas, UC3M, Spain

Title: New perspectives on Laguerre-Sobolev type orthogonal polynomials

Abstract:  Our viewpoint sheds some new light on the asymptotic behavior of the Laguerre-Sobolev type monic orthogonal polynomial sequences, considering the perturbation of the Laguerre weight supported on the negative semi-axis of the real line. We study the outer relative asymptotic of these polynomials with respect to the standard Laguerre polynomials. The analogue of the Mehler-Heine formula as well as a Plancherel-Rotach formula for the rescaled polynomials are given. Finally, we analyze the behavior of their zeros in terms of their dependence on $N$.

Thursday, September 8, 2011. 4:00 pm. Room 2.2.D08

Speaker: Evguenii Rakhmanov, University of South Florida, USA

Title: Zeros of Heine-Stieltjes Polynomials and a general Modulii Problem

Abstract: The limit distribution of zeros of HS polynomials may be described as (positive) critical measures -critical points of an energy functional with respect to local point variation. A constructive characterization of the critical measures may be given in terms of closed quadratic differentials. It turns out that the same class of quadratic differentials solves one of the classical problems in geometric function theory - the problem of extremal partition of the plane with respect to a certain family of curves. This connection presents an independent interest and may be used in the investigation of both problems.

Wednesday, 08 July 2020 12:16:06