Local Informations

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Title: Funciones internas en el Espacio de Dirichlet

AbstractEn un espacio de Hilbert de funciones analíticas $H$, una función $f$ es \emph{interna} si satisface cierta sucesión de condiciones de ortogonalidad. Este concepto permite estudiar la estructura de espacios invariantes de $H$. En esta charla estudiamos el caso en el que $H$ es el espacio de Dirichlet, y damos una caracterización de las mismas en términos del operador de multiplicación que definen.

Thursday, October 26,  2017, 16:00. Room 2.2.D08

Title: On Semiclassical Families of Bivariate Orthogonal Polynomials

Abstract: Orthogonal polynomials in two variables are studied as the natural generalization of orthogonal polynomials in one variable. Nevertheless, much work needs to be done in order to consider the theory of bivariate orthogonal polynomials as complete as the univariate case. In this work, we focus on extending well-known properties of univariate semiclassical orthogonal polynomials to the bivariate case. We also study algebraic and differential properties of a class of orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Finally, we extend the definition of coherent pairs of quasi-definite moment functionals to the bivariate case and deduce some of its consequences.

Past seminars

Title:Classical perturbations for matrices of linear functionals

Abstract: This thesis is focused on the study  of  matrix transformations of  matrices with  linear  functionals as entries. In particular, we study the Christoffel, Geronimus, and Geronimus-Uvarov transformations,  as well as,  their relation  with scalar orthogonal polynomials satisfying a higher order recurrence relation.

Thursday, June 22,  2017, 16:00. Room 2.2.D08

Speaker: Gerardo Ariznabarreta,  (U. Complutence)

Title: Polinomios biortogonales generalizados. Una perspectiva desde los Sistemas Integrables.

Abstract:  El problema de factorización LU de una matriz puede tomarse como punto de partida para el estudio, tanto de los polinomios ortogonales como para acercarse a la teoría de los sistemas integrables. Utilizando esta técnica se compararán las transformaciones de Christoffel en los casos escalar, matricial y multivariable y, a continuación, las conexiones entre estos tipos de ortogonalidad y las jerarquías integrables tipo Toda.

Thursday, June  08,  2017. Room 2.2.D08

Speaker: .Leonardo Rendon, Departamento de Matemáticas Universidad Nacional de Colombia en Bogotá

Title:  Applications of the compensated compactness method onhyperbolic conservation systems

Abstract:: In this talk, I would like to introduce the applications of the compensated compactness method on hyperbolic conservation systems of two equations. I will   present  some results from our research group.

Thursday, May  25,  2017, 16:00. Room 2.2.D08

Speaker:  Ernesto Correa Velandia, Universidad Carlos III de Madrid

Title:  Nonlocal operators of order near zero

Abstract:: We study Dirichlet forms defined by nonintegrable Lévy kernels whose singularity at the origin can be weaker thant that of any fractional Laplacian. We show some properties of the associated Sobolev type spaces in a bounded domain, such as symmetrization estimates, Hardy inequalities, or the inclusion in some Lorentz space. We then apply these properties to study the associated nonlocal operator L and the Dirichlet and Neumann problems related to the equation Lu=f(x) and Lu=f(u) in $\Omega$.

Thursday, May  18,  2017, 16:00. Room 2.2.D08

Speaker: Wilfredo Urn¡bina Romero (Roosevelt University, Chicago, IL, USA)

Title: Transference results from the $L^p$ continuity of operators in the Jacobi case to the $L^p$ continuity of operators in the Hermite and Laguerre case.

Abstract: Using the well known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials we develop a transference method to obtain the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the Laguerre-Riesz transform from the $L^p$-continuity of the Jacobi-Riesz transform, in dimension one as well as the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the Laguerre-Riesz transform from the $L^p$-continuity of the Jacobi-Riesz transform. The case of the corresponding Littlewood-Paley g-functions will also be discussed.

Thursday, May  11,  2017, 17:00. Room 2.2.D08

Speaker: Daniel A. Rivero Castillo, Universidad Carlos III de Madrid

Title: Iterated Integrals of Orthogonal Polynomials and Applications.

Abstract::Algebraic and analytical properties of families of polynomials obtained by iterated integration  until a fixed order m, of families of orthogonal polynomials with respect to a measure supported on the real line or an arc of the unit circle.

Edge detection in gray-scale images based on approximating the derivatives of the function image using the Krawtchouk orthogonal polynomials.

Tuesday, April  25,  2017, 17:00. Room 2.2.D08

Speaker: .Bei-Bei Zhu, Chinese Academy of Sciences, Beijing & Universidad Carlos III de Madrid

Title:  A stroboscopic averaging algorithm for highly oscillatory delay problems

Abstract:: For highly oscillatory delay differential system, the presence of the fast-frequency oscillation makes numerical simulations so costly that it is better to average out the fast oscillations by using the averaging method before applying the numerical method. However, the analytic expression of the averaged system may be difficult or impossible to obtain. The stroboscopic averaging method is a technique that approximates the averaged solution by using only the originally given system. Error bounds and numerical results will be provided.

Thursday,  March  2,  2017, 17:00. Room 2.2.D08

Speaker: .Plamen Iliev, School of Mathematics, Georgia Institute of Technology

Title:  Hypergeometric and multiple orthogonal polynomials bases for the Alpert multiresolution analysis

Abstract::I will describe two explicit bases for the Alpert multiresolution analysis and discuss their properties. The first one consists of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials, while the second basis is related to type I Legendre-Angelesco multiple orthogonal polynomials. The talk will based on joint works with Jeff Geronimo and Walter Van Assche.

Thursday,  February  23,  2017, 17:00. Room 2.2.D08

Speaker: .Plamen Iliev, School of Mathematics, Georgia Institute of Technology

Title:  Krall commutative algebras of differential operators

Abstract:: In 1938, Krall posed the general problem to construct and classify all families of orthogonal polynomials which are eigenfunctions of a differential operator of arbitrary order, which is independent of the degree index. General bispectral techniques based on the Darboux transformation led to a large collection of solutions to Krall’s problem. In this talk, I will discuss yet another method motivated by solitons, which can be used to construct and characterize the commutative algebras of differential or q-difference operators for Krall polynomials.

Thursday,  January  26,  2017, 16:00. Room 2.2.D08

Speaker: .Luis Garza  (U. Colima)

Title:  On a relation between Hurwitz and orthogonal polynomials

Abstract:: Abstract: A linear control system is stable if its characteristic polynomial is Hurwitz. In this talk, we present some relations between Hurwitz and orthogonal polynomials that could be useful to study the stability of linear systems. In particular, we construct families of Hurwitz polynomials by using sequences of orthogonal polynomials and obtain some interesting properties.

Thursday,  January 19,  2017, 16:00. Room 2.2.D08

Speaker: Lino Gustavo Garza (UC3M).

Title: Analytic Properties of Polynomials Orthogonal with respect to Coherent Measures Supported on the Unit Circle

Abstract::This work presents a study of orthogonal polynomials from a matrix point of view. We deal with semiclassical and coherent orthogonal polynomials. We also consider the dierence and q-dierence operators. We also study the (0,2)-coherent pairs of measures of the second kind supported on the unit circle.

Tuesday, January 10 2017, 16:00. Room 2.2.D08

Speaker: Herbert Dueñas Ruiz (Universidad Nacional de Colombia)

Title: Sobolev orthogonal polynomials on product domains in several variables.

Abstract: Using the ideas presented in [1], we study the
polynomials of several variables orthogonal with respect to the inner
product:

_S=c \int_{\Omega }  \nabla ^{2} f(x,y) \cdot nabla ^{2}g(x,y)   W(x,y) dydx+\lambda  f(c1,c2) g(c1 ,c2),

where (c1, c2) is some corner point in \Omega =[a1,b1] x [ a2,b2], \lambda >0, and c=1 /  \int_{\Omega } W(x,y) dxdy.
Two examples are presented using Laguerre and Gegenbauer polynomials.

[1] L. Fernández, F. Marcellán, T. Pérez, M. Piñar and Y. Xu, Sobolev orthogonal polynomials on product domains, Jour. Comp. App. Math. Vol 284. No 5 (2015), 202-215.

Thursday, January 12 2017, 16:00. Room 2.2.D08

Speaker: Omar Rosario Cayetano (UC3M)

Title: Graphs with small hyperbolicity constant andhyperbolic minor graphs.

Abstract: If X is a geodesic metrix space and x1, x2, x3 in X, a geodesic triangle T={x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X.

The space X is delta-hyperbolic (in the Gromov sense) if any side of T is contained in a delta-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by delta(X) the sharp hyperbolicity constant of X, i.e., delta(X)=inf{delta>=0: X is delta-hyperbolic}. In this work we study the graphs with small hyperbolicity constant, i.e., the graphs which are like trees (in the Gromov sense).

We obtain simple characterizations of the graphs G with delta (G)=1 and delta(G)=5/4. A graph H is a "minor" of a graph G if a graph isomorphic to H can be obtained from G by contracting some edges, deleting some edges, and deleting some isolated vertices.

One of the main aims in this work is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph G/e obtained from the graph G by contracting an arbitrary edge e from it.

We also prove that H is hyperbolic if and only if G is hyperbolic, for many minors H of G, even if H is obtained from G by contracting and/or deleting infinitely many edges.

Thursday, December 15 2016, 16:00. Room 2.2.D08

Speaker: Roberto S. Costas-Santos (U. Alcalá)

Title: Matrices totally symmetric relative to a tree.

Abstract: A matrix is called totally positive (TP) if every minor of it is positive. It is known that for a TP matrix, the eigenvalues are positive  and distinct and the eigenvector associated with the smallest eigenvalue is totally nonzero and has an alternating sign pattern. We will be interested in submatrices of a given matrix that are TP, or  permutation similar to TP. Thus, we will be interested in permuted submatrices, identified by ordered index lists. For a given labelled tree T on n vertices, we say that A is T-TP if, for every  path P in T, A[P] is TP. J. Garloff relayed to us an old conjecture of A. Neumaier that for any tree T, the eigenvector associated with the smallest eigenvalue of a T-TP matrix should be signed according to the labelled tree T. We refer to this as the T-TP conjecture''. In this talk we prove that the conjecture is false, giving some examples and present. certain weakening of the TP hypothesis is shown to yield a similar conclusion, i.e. the eigenvector, associated with the smallest eigenvalue, alternates in sign as in the  tree.This is a joint work with Charles R. Johnson, and Boris Tadchiev.

Thursday, December 01 2016, 16:00. Room 2.2.D08

Speaker: Yanely Zaldivar Gerpe ( UC3M)

Title: Inverse results for the m-th row of Incomplete Padé Aproximants.

Abstract: We study inverse type results for incomplete Padé approximants of analytic functions under the assumption that the sequence of denominators of the approximating rational functions have limit. Such results allow to describe the region to which the analytic function can be extended meromorphically, determine the location and order of the poles in this region, and detect some singularities on the boundary. These results are applied to the study of Hermite-Padé approximants; that is interpolating vector rational functions of vectors of analytic functions. We also extend to row sequences of incomplete Padé approximants some classical results, due to Hadamard and Ostrowski, related with the overconvergence of subsequences of Taylor polynomials and the analytic properties of the limit function under the presence of gaps in the power series.

Thursday, November 24 2016, 16:00. Room 2.2.D08

Speaker: Abel Díaz González ( UC3M)

Title: Sobolev extremal polynomials with respect to mutually singular measures.

Abstract: Extremal polynomials with respect to a Sobole-type p-norm, with 1< p < \infty and measures supported on compact subsets of the real line, are considered. For a wide class of such extremal polynomials with respect to measures mutually singular, it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved, the asymptotic critical point distribution is studied. We also find the nth root asymptotic behavior of the corresponding sequence of the derivatives of Sobolev extremal polynomials.

Thursday, November 10 2016, 16:00. Room 2.2.D08

Speaker: Alfredo Toledano ( Universidad Complutense de Madrid )

Title: CMV biorthogonal Laurent polynomials: Christoffel formulas for Christoffel and Geronimus perturbations

Abstract: Quasidefinite sesquilinear forms for Laurent polynomials in the complex plane and corresponding CMV biorthogonal Laurent polynomial families are studied, considering bivariate linear functionals. We have discussed two possible Christoffel transformations of these linear functionals: Christoffel perturbation and Geronimus perturbation. The last one with the addition of appropriate masses.

The aims are getting the connection formulas for the CMV biorthogonal Laurent polynomials and its norms, thanks to Christoffel-Darboux kernels, second kind functions and mixed Chirstoffel-Darboux kernels.

For prepared Laurent polynomials, i.e., of the form L(z)=L_n z^n+...+L_{-n} z^{-n}, L_n L_{-n} \ne 0, these connection formulas lead to quasideterminantal (quotient of determinants) Christoffel formulas.

Finally, we present curves as examples, such as: the real line, the circle, the Cassini oval and the cardioid.

Thursday, November 03 2016, 16:00. Room 2.2.D08

Speaker: Luis Alejandro Molano Molano (U. Pedagógica Tecnológica de Colombia, Duitama, Colombia)

Title: On symmetric (1,1)-coherent pairs.

Abstract: In this talk we will discuss briefly some basic notions about symmetric (1,1)-coherent pairs. We will exhibit explicitly some of them, based on the symmetrization method for linear functionals. Finally we are going to treat some particular cases relative to classical measures and we will present open questions that are part of our current research.

Thursday, October 27 2016, 16:00. Room 2.2.D08

Speaker: José Javier Segura Sala (U. de Cantabria)

Title: Computation of asymptotic expansions of turning point problems via Cauchy's theorem.

Abstract: Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two infinite series, the coefficients of which are usually difficult to compute. By considering the series as asymptotic expansions for two explicitly defined analytic functions, Cauchy's integral formula is employed to compute the coefficient functions to high order of accuracy. The method employs a certain exponential form of Liouville-Green expansions for solutions of the differential equation, as well as for the Airy function. We illustrate the use of the method for the computation of Bessel functions and Laguerre polynomials of complex argument.

Thursday, October 20 2016, 16:00. Room 2.2.D08

Speaker: Roberto S. Costas-Santos (U. de Alcalá)

Title: Orthogonality relations of Al-Salam-Carlitz  for general parameters.

Abstract: In this talk we describe the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials $U^{(a)}_n(x;q)$ when the parameters a and q are not necessarily real nor 'classical', i.e., the linear functional u with respect to such polynomial sequence is quasi-definite and not positive definite.

We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam-Carlitz polynomials $U_n^{(a)}(x;q)$ of degree $n$ up to a constant factor. We also obtain a generalization of the unique generating function for these polynomials.

This is a joint work with Howard S. Cohl, and Wenqing Xu.

Thursday, October 06 2016, 16:00. Room 2.2.D08

Speaker: José Manuel Rodríguez (UC3M)

Title: La estrategia de Kelly en apuestas deportivas e inversiones en bolsa: algunos consejos de inversión.

Abstract: En esta conferencia se hará una revisión histórica de la estrategia de Kelly, sus generalizaciones y sus aplicaciones en apuestas deportivas e inversiones. Se discutirán también sus ventajas e inconvenientes prácticos, y finalmente se expondrán las aportaciones del conferenciante en este tema.

Thursday, September 22 2016, 16:00. Room 2.2.D08

Speaker: Abel Díaz (UC3M)

Title: Sobolev extremal polynomials with respect to mutually singular measures.

Abstract: Extremal polynomials with respect to a Sobole-type p-norm, with 1< p < \infty and measures supported on compact subsets of the real line, are considered. For a wide class of such extremal polynomials with respect to measures mutually singular, it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved, the asymptotic critical point distribution is studied. We also find the nth root asymptotic behavior of the corresponding sequence of the derivatives of Sobolev extremal polynomials.

Tuesday, September 20 2016, 16:00. Room 2.2.D08

Speaker: Alfredo Deaño (University of Kent, UK)

Title: From Painlevé transcendents to random matrices and back.

Abstract: Painlevé transcendents have found a wide variety of applications in the last decades, including the description of transitions in the global and local behavior of the spectrum of certain ensembles of random matrices, as the size of the matrices N tends to infinity. When the classical ensembles such as the Gaussian or Laguerre Unitary Ensembles undergo some deformations, one technique to study the changes in the global and local picture of the spectrum and the partition function is via orthogonal polynomials, which may not be classical or defined on the real line anymore. Additionally, some quantities related to this non-classical orthogonal polynomials, such as the coefficients appearing in the recurrence relations, can belong to some specific hierarchies of solutions of differential equations of Painlevé type. In this talk we will illustrate these connections using two examples: a deformation of GUE with a cubic term and a deformation of LUE that makes use of semi-classical Laguerre polynomials on R^+.

Last Updated on Wednesday, 11 October 2017 16:58

Saturday, 04 December 2021 12:39:40