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Written by Luis E. Garza Gaona   
Monday, 12 January 2009 23:55

 Luis E. Garza Gaona

Profesor Investigador Titular A

Universidad de Colima

Facultad de Ciencias

Bernal Díaz del Castillo No. 340

Colima, Colima, México

Despacho: Edificio B

Teléfono: +52 312 316 1135 Ext. 48008

FAX: +52 312 316 0000

E-Mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it

Webpage: https://luis-garza.blog.ucol.mx/p/home.html

 

 Luis Garza Gaona

 

 


 List of Publications

  1. Lino G. Garza, Luis E. Garza, Edmundo J. Huertas, "On differential equations associated with perturbations of orthogonal polynomials on the unit circle", Mathematics, 8(2), 246 (2020).
  2. Edinson Fuentes, Luis E. Garza, "CMV block matrices for symmetric matrix measures on the unit circle", Linear Algebra Appl., 587, 314-333 (2020).
  3. Edinson Fuentes, Luis E. Garza, "Matrix moment perturbations and the inverse Szego  matrix transformation", Rev. Union Mat. Argent., 60(2), 573-593 (2019).
  4. Alejandro Arceo, Luis E. Garza, Gerardo Romero, "Robust stability of Hurwitz polynomials associated with modified classical weights", Mathematics, 7(9), 818 (2019).
  5. Luis E. Garza, Edmundo Huertas, Francisco Marcellán, "On Freud-Sobolev type orthogonal polynomials", Afrika Mat., 30(3-4), 505-529 (2019).
  6. Noé Martínez, Luis E. Garza, Baltazar Aguirre-Hernández, "On sequences of Hurwitz polynomials related to orthogonal polynomials", Linear and Multilinear Algebra, 67(11), 2191-2208 (2019).
  7. Herbert Dueñas, Luis E. Garza, Paul Villamil Hernández, "Polinomios ortogonales de Freud Sobolev. Un caso no diagonal", Jairo Charris. Iván Castro y Fernando Zalamea Eds. Serie Memorias Grandes Maestros 2, Universidad Nacional de Colombia, Bogotá, Colombia, 2018. 159-192.
  8. Juan Carlos García-Ardila, Luis E. Garza, Francisco Marcellán, "A canonical Geronimus transformation for matrix orthogonal polynomials", Linear and Multilinear Algebra, 66(2), 357-381 (2018). 
  9. Abdon Choque-Rivero, Luis E. Garza, "Matrix orthogonal polynomials associated with perturbations of Toeplitz matrices", Russian Math., 61, 57-69, (2017).
  10. Juan Carlos García-Ardila, Luis E. Garza, Francisco Marcellán, "An extension of the Geronimus transformation for orthogonal matrix polynomials on the real line", Mediterr. J. Math., 13, 5009-5032 (2016).
  11. Luis E. Garza, Francisco Marcellán, "Orthogonal polynomials and perturbations of measures supported on the real line and on the unit circle. A matrix perspective", Expositiones Math., 34, 287-326 (2016).
  12. Edinson Fuentes, Luis E. Garza, "On a finite moment perturbation of linear functionals and the inverse Szego transformation", Revista Integración, 34 (1), 39-58 (2016).
  13. Lino G. Garza, Luis E. Garza, F. Marcellán, Natalia C. Pinzón-Cortés, "A matrix characterization for the Dv-Semiclassical and Dv-Coherent orthogonal polynomials", Linear Alg. Appl., 487, 242-259 (2015).
  14. Edinson Fuentes, Luis E. Garza, "Analysis of perturbations of moments associated with orthogonality linear functionals through the Szego transformation", Revista Integración, 33 (1), 61-82 (2015).
  15. Lino G. Garza, Luis E. Garza, F. Marcellán, Natalia Pinzón-Cortés, "A matrix characterization for the semiclassical and coherent orthogonal polynomials",  App. Math. Comput., 256, 459-471 (2015).
  16. Herbert Dueñas, Luis E. Garza, Miguel Piñar, "A higher order Sobolev-type inner product for orthogonal polynomials in several variables", Numer. Algor., 68, 35-46 (2015).
  17. Abdón Choque-Rivero, Luis E. Garza, "Moment pertubation of matrix polynomials", Integral Transforms and Special Functions, 26,  3, 177-191 (2015).
  18. K. Castillo, L. Garza and F. Marcellán, "On a direct Uvarov-Chihara problem and some extensions", Analytic Number Theory, Approximation Theory, and Special Functions - In honor of Hari M. Srivastrava (K. Alladi, G. V. Milovanovic, M. Th. Rassias, eds). Series: Springer Optimization and its Applications, Vol XI, Springer Verlag, Berlin - Heidelberg - New York, 2014.
  19. Luis Garza, Francisco Marcellán, and Natalia C. Pinzón-Cortés, "(1,1)-Coherent pairs on the unit circle", Abstract and Applied Analysis, vol. 2013, Article ID 307974, 8 pages, (2013).
  20. K. Castillo, D.K. Dimitrov, L. E. Garza, F.R. Rafaeli, “Perturbations on the subdiagonal of Hankel matrices”, App. Math. And Comput., 221, 444—552 (2013).
  21. Herbert Dueñas, Luis Garza, Juan C. García, Guillermo A. Ramírez, “The diagonal general case for Laguerre-Sobolev orthogonal polinomials. Revista Colombiana de Matemáticas, 47, No.1, 39—66 (2013).
  22. Herbert Dueñas, Luis Garza, “Jacobi-Sobolev-type orthogonal polinomials: Holonomic equation and electrostatical interpretation - a non diagonal case”, Integral Trans. Spec. Functions, Vol. 24, No. 1, 70—83, 2013.
  23. Kenier Castillo, Luis Garza, Francisco Marcellán, “Asymptotic behavior of Sobolev orthogonal polynomials on the unit circle”, Integral Trans. Spec. Functions, Vol. 24, No. 1, 23—28, 2013.
  24. Herbert Dueñas, Luis Garza, “Perturbations of Laguerre-Hahn linear functionals by Dirac delta derivatives”, Boletín de Matemáticas, Univ. Nacional de Colombia, Vol. 19, No. 1, 65—90, 2012.
  25. Kenier Castillo, Luis E. Garza, Francisco Marcellán, "Sobolev orthogonal polynomials on the unit circle: Hessenberg matrices and zeros", Proceedings of the 12th ICCMMSE, Editor: J. Vigo-Aguiar, Vol. 1, 303-307 (2012).
  26. Kenier Castillo, Luis Garza, Francisco Marcellán, “Zeros of Sobolev orthogonal polynomials on the unit circle”, Numer. Algor, Vol. 60, N0. 4, 669-681, (2012).
  27. Kenier Castillo, Luis Garza, Francisco Marcellán, “A new linear spectral transformation associated with derivatives of Dirac linear functionals”, J. Approx. Theory, Vol. 163, No. 12, 1834-1853, 2011.
  28. Kenier Castillo, Luis Garza, Francisco Marcellán, “Perturbations on the subdiagonals of Toeplitz matrices”, Linear Algebra Appl., 434, (2011), 1563-1579.
  29. Herbert Dueñas, Luis Garza, “Asymptotic behaviour of the Jacobi-Sobolev orthogonal polinomials. A non diagonal case”, Revista de la Academia Colombiana de Ciencias, Vol. XXXIV, 133, (2010), 529-539.
  30. Kenier Castillo, Luis Garza, Francisco Marcellán, “Linear spectral transformations, Hessenberg matrices and orthogonal polynomials”, Rend. Circ. Mat. Palermo, (II), 82 (2010), 3-26.
  31. Luis Garza, Francisco Marcellán, “Quadrature rules on the unit circle. A survey”, Recent Trends in Orthogonal Polynomials and Approximation Theory. J.Arvesú, F. Marcellán, and A. Martínez Finkelshtein Editors. Contemporary Mathematics. Vol. 507. Amer. Math. Soc. Providence, RI. 2010. 113-140.

  32. Luis Garza, Javier Hernández, Francisco Marcellán, "Orthogonal Polynomials on the unit circle. The Geronimus transformation", Journal of Computational and Applied Mathematics233 (2010), 1220-1231.
  33. Kenier Castillo, Luis Garza, Francisco Marcellán, “Laurent polynomial perturbations of linear functionals. An inverse problem.”, Electronic Transactions on Numerical Analysis, Vol. 36 (2010), 83-98.
  34. Luis Garza, Francisco Marcellán, “Szego transformations and rational spectral transformations for associated polynomials”, Journal of Computational and Applied Mathematics233 (2009), 730-738.
  35. Luis Garza, Francisco Marcellán, “Linear spectral transformations and Laurent polynomials”, Mediterranean Journal of Mathematics6 (2009) 273-289.
  36. Luis Garza, Francisco Marcellán, “Verblunsky parameters and linear spectral transformations”, Methods and Applications of Analysis, 16 (2009), 069-086.
  37. Luis Garza, Francisco Marcellán, “Szego transformations and Nth order associated polynomials on the unit circle”, Computers and Mathematics with Applications57 (2009), 659-671.
  38. Luis Garza, Francisco Marcellán, “Orthogonal polynomials and rational spectral transformations”, Mathematical Physics and Field Theory, M Asorey, J. V. García Esteve, M. F. Rañada and J. Sesma Editors. Prensas Universitarias de Zaragoza, Spain, 2009. 239-248.
  39. Luis Garza, Javier Hernández, Francisco Marcellán, "Spectral transformations of measures on the unit circle and the Szego transformation”, Numerical Algorithms49 (2008) 169-185.

 

 

 


 Presentations


 

Invited talks:


  • On some electrostatic models associated with zeros of orthogonal polynomials, Meeting on Geometry and Physics UASLP 2019, UASLP, San Luis Potosí, México (January 2019)
  • Spectral transformations of orthogonal polynomials. A matrix perspective, VI Iberoamerican Workshop in Orthogonal Polynomials and Applications, Universidade Federal do Triângulo Mineiro (UFTM), Uberaba, Brazil (May 2017).
  • A higher order Sobolev-type inner product for orthogonal polynomials in several variables, Selected Topics in Mathematical Physics, IMATE Cuernavaca, México (November 2016)
  • Polinomios ortogonales: Una introducción a la teoría de transformaciones espectrales, Encuentro Nacional de Jóvenes Investigadores en Matemáticas, CDMX, México (December 2015)
  • A matrix approach for the semiclassical and coherent orthogonal polynomials, 1st Joint Meeting IMU-SMM, Oaxaca, México (September 2015).
  • On a matrix approach for semiclassical orthogonal polynomials, BIRS-CMO Orthogonal and Multiple Orthogonal Polynomials, Oaxaca, México (August 2015).
  • On orthogonal polynomials associated with perturbations of Hankel matrices, FoCM, Montevideo, Uruguay (December 2014).
  • Polinomios ortogonales asociados a perturbaciones de momentos, 3er. Encuentro Conjunto de la RSME y la SMM, Zacatecas, México (September 2014).
  • Multivariate orthogonal polynomials: algebraic and analytic properties, XXIV Escuela Nacional de Optimización y Análisis Numérico, CIMAT, Guanajuato, México (May 2014).
  • On non standard perturbations of classical orthogonal polynomials, 3rd. International Workshop on Analysis, Differential Equations, and Control Theory, IFM Morelia, México (February 2014).
  • Sobolev-type orthogonality: Algebraic and asymptotic properties, Mini-Conferencia de Análisis Matemático, Puebla, México (November 2013).
  • Sobolev orthogonal polynomials on the unit circle: asymptotic properties and zeros, Tercer Encuentro Iberoamericano de Polinomios Ortogonales y Aplicaciones (EIBPOA3), San José do Rio Preto, Brazil (May 2013).
  • Perturbation of Laguerre-Hahn class linear functionals by Dirac delta derivatives, International Workshop in Analysis, Differential Equations, and Contro Theory, Morelia, Michoacán, México (January 2012).
  • Polinomios Ortogonales y perturbaciones de matrices de Toeplitz. Primer EIBPOA, Bogotá, Colombia (June 2011).
  • Spectral transformations of orthogonal polynomials: A connection to integrable systems. Jairo Charris Seminar 2010. Santa Marta, Colombia. (August 2010).

 

Contributed talks:


  • Symmetric matrix measures on the unit circle: factorization of CMV matrices, Sixth International Conference in Mathematics and its Applications, Puebla, México (September 2019).
  • CMV block matrix for symmetric matrices measures on the unit circle,  15th. International Symposium in Orthogonal Polynomials, Special Functions and its applications, Hagenberg, Austria, (July 2019).
  • On asymptotic properties of Sobolev orthogonal polynomials on the unit circle, 13th OPSFA, Gaithersburg, Unites States (June 2015).
  • Coherence relations for orthogonal polynomials on the unit circle, Constructive functions 2014, Nashville, United States (May 2014)
  • On asymptotic properties of multivariate orthogonal polynomials, International Symposium on Orthogonality, Quadrature, and related topics, Puerto de la Cruz, Tenerife, Spain (January 2014).
  • Orthogonal polynomials associated with coherent pairs, XI International Symposium on Approximation and Optimization at the Caribbean, Puebla, México (October 2013).
  • (1,1)-Coherent pairs on the unit circle, XIX Congreso Colombiano de Matemáticas, Barranquilla, Colombia (July 2013).
  • Sobolev orthogonal polynomials on the unit circle: asymptotic properties and zeros, 12th Orthogonal Polynomials, Special Functions and Applications (OPSFA), Sousse, Tunisia (March 2013).
  • Sobolev orthogonal polynomials on the unit circle: Zeros properties, XLV Congreso Nacional de Matemáticas, Querétaro, México (October 2012).
  • Perturbation of Laguerre-Hahn class linear functionals by Dirac delta derivatives, 11th Orthogonal Polynomials, Special Functions and Applications (OPSFA), Leganés, Madrid (August 2011).
  • Perturbations of OPUC by the addition of Dirac delta derivatives. International Conference on Applied Mathematics and Informatics, San Andrés Island, Colombia (December 2010).
  • Perturbations on the subdiagonal of Toeplitz matrices. I Jaén Conference on Approximation Theory, Úbeda, Jaén, Spain. (July 2010).
  • A diagonal perturbation of a Toeplitz matrix. Second South Texas Algebra Colloquium, South Padre Island, TX. (November 2009).
  • Laurent polynomial perturbation of linear functionals. An inverse problem.10th Symposium on Orthogonal Polynomials, Special Functions and Applications, Lovain, Belgium (July 2009).
  • Quadrature rules on the unit circle. Applications in frequency analysis. International Workshop in Approximation Theory and Signal Analysis, Lindau, Germany (March 2009).
  • Linear Spectral Transformations and Verblunsky Coefficients. International Workshop in Orthogonal Polynomials and Applications (IWOPA’08), Leganés, Spain (September 2008).
  • Szego transformation and rational spectral and transformations for associated polynomials. IX Internacional Conference on Optimization and Approximation in the Caribbean, San Andrés Island, Colombia (February 2008).
  • Rational Spectral Transformations of Measures on the Unit Circle and the Szego Transformation, Symposium on Special Functions, Information Theory and Mathematical Physics, Granada, Spain (September 2007).
  • Rational Spectral Transforms of Measures on the Unit Circle. 9th. International Workshop on Orthogonal Polynomials, Special Functions and Applications (OPSFA), Marseille, France (July 2007).
  • Spectral Transformations of Measures on the Unit Circle and the Szego Transformation. 10th European Workshop on Applications and Generalizations of Complex Analysis, Coimbra, Portugal (June 2007).

 

Seminars:


  • Orthogonal polynomials: spectral transformations and matrix factorizations, Séminaire Analyse Numérique - Equations aux Dériveés Partielles at Lab. Paul Painlevé, Lille, France (May 2019).
  • Matrix characterizations of orthogonality on the real line, Coloquio FMAT-CIMAT, UADY, Mérida, México (January 2019)
  • Sobre la conexión de la teoría de polinomios ortogonales con la estabilidad de sistemas lineales, Coloquio del Instituto de Matemáticas, UNAM, CDMX, México (November 2017)
  • Polinomios ortogonales y su relación con teoría de control, Seminario UAT-RODHE, Universidad Autónoma de Tamaulipas, Reynosa, México (June 2017)
  • Polinomios ortogonales, una introducción a la teoría de transformaciones espectrales, Seminario del Departamento de Matemáticas, Universidad de Alcalá de Henares, España (February 2017)
  • On a relation between Hurwitz and orthogonal polynomials, GAMA Seminar,  Universidad Carlos III de Madrid, España (January 2017)
  • Sobre perturbaciones de matrices de momentos asociadas a medidas de ortogonalidad, Coloquio del Depto. de Matemáticas, UNAL, Colombia (December 2014).
  • Propiedades generales de polinomios ortogonales en la circunferencia unidad, Seminario de Polinomios Ortogonales, U. Nacional de Colombia, Colombia (August 2014).
  • Polinomios ortogonales en varias variables: propiedades algebraicas y analíticas, Seminario del Área de Ecuaciones Diferenciales y Geometría, UAM Iztapalapa, México (February 2014).
  • Una introducción a los polinomios ortogonales. Teoría de perturbaciones, Seminario del Posgrado en Matemáticas, UAM Iztapalapa, México (February 2014).
  • Orthogonal polynomials associated with coherent measures, Seminario IMUS, Universidad de Sevilla, Spain (February 2014).
  • Orthogonal polynomials on the unit circle and perturbations of Toeplitz Matrices, Colloquio Depto. De Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia (August 2012).
  • Polinomios ortogonales y perturbaciones de matrices de Toeplitz. Coloquio del Posgrado Conjunto en Ciencias Matemáticas UNAM-UMSNH, Morelia, México (October 2010).
  • Transformaciones espectrales y polinomios ortogonales: un enfoque matricial. Seminario de Geometría Algebráica IFM-UMSNH, Morelia, México (October 2010).
  • Polinomios ortogonales en la circunferencia unidad y transformaciones espectrales. Seminario CUICBAS, Universidad de Colima, Colima, México. (April 2010).
  • Spectral transformations for OPUC and factorization of Hessenberg matrices. Mathematics Seminar, UTB/TSC, Brownsville, TX. (November 2009).
  • Orthogonal polynomials on the unit circle and spectral transformations. Integrable Systems Seminar, UTPA, Edinburg, TX. (October 2009).
  • Rational spectral transformations and the Szego transformation. Seminario Rubio de Francia, Zaragoza, Spain (May 2008).

 

Last Updated on Saturday, 15 February 2020 17:05