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Publications


  1. Edinson Fuentes, Luis E. Garza, "Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle", Math. Slovaca (2021). In press.
  2. H. Dueñas, E. Fuentes, Luis E. Garza, "On a Christoffel transformation for matrix measures supported on the unit circle", Comput. Methods Funct. Theory (2021). DOI: 1017/s40315-020-00324-x. In press.
  3. E. Fuentes, L. E. Garza, H. Dueñas, "On the Szego transformation for some spectral transformations of matrix measures", J. Math. Anal. Appl. 499, 125036 (2021). 
  4. H. Dueñas, E. Fuentes, Luis E. Garza, "Matrix Uvarov transformation on the unit circle: asymptotic properties", Bull. Malays. Math. Sci. Soc., 44, 279-315 (2021). 
  5. Luis E. Garza, "On Sobolev-type perturbations of classical orthogonal polynomials", Matemáticas y sus aplicaciones 15, BUAP, México (2020).
  6. Luis E. Garza, Noé Martínez, Gerardo Romero, "New stability criteria for discrete linear systems based on orthogonal polynomials", Mathematics, 8(8), 1322 (2020).
  7. 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).
  8. Edinson Fuentes, Luis E. Garza, "CMV block matrices for symmetric matrix measures on the unit circle", Linear Algebra Appl., 587, 314-333 (2020).
  9. Edinson Fuentes, Luis E. Garza, "Matrix moment perturbations and the inverse Szego  matrix transformation", Rev. Union Mat. Argent., 60(2), 573-593 (2019).
  10. Alejandro Arceo, Luis E. Garza, Gerardo Romero, "Robust stability of Hurwitz polynomials associated with modified classical weights", Mathematics, 7(9), 818 (2019).
  11. Luis E. Garza, Edmundo Huertas, Francisco Marcellán, "On Freud-Sobolev type orthogonal polynomials", Afrika Mat., 30(3-4), 505-529 (2019).
  12. 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).
  13. 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.
  14. 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). 
  15. Abdon Choque-Rivero, Luis E. Garza, "Matrix orthogonal polynomials associated with perturbations of Toeplitz matrices", Russian Math., 61, 57-69, (2017).
  16. 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).
  17. 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).
  18. 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).
  19. 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).
  20. 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).
  21. 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).
  22. 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).
  23. Abdón Choque-Rivero, Luis E. Garza, "Moment pertubation of matrix polynomials", Integral Transforms and Special Functions, 26,  3, 177-191 (2015).
  24. 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.
  25. 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).
  26. 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).
  27. 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).
  28. 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.
  29. 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.
  30. 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.
  31. 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).
  32. Kenier Castillo, Luis Garza, Francisco Marcellán, “Zeros of Sobolev orthogonal polynomials on the unit circle”, Numer. Algor, Vol. 60, N0. 4, 669-681, (2012).
  33. 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.
  34. Kenier Castillo, Luis Garza, Francisco Marcellán, “Perturbations on the subdiagonals of Toeplitz matrices”, Linear Algebra Appl., 434, (2011), 1563-1579.
  35. 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.
  36. Kenier Castillo, Luis Garza, Francisco Marcellán, “Linear spectral transformations, Hessenberg matrices and orthogonal polynomials”, Rend. Circ. Mat. Palermo, (II), 82 (2010), 3-26.
  37. 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.
  38. Luis Garza, Javier Hernández, Francisco Marcellán, "Orthogonal Polynomials on the unit circle. The Geronimus transformation", Journal of Computational and Applied Mathematics, 233 (2010), 1220-1231.
  39. 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.
  40. Luis Garza, Francisco Marcellán, “Szego transformations and rational spectral transformations for associated polynomials”, Journal of Computational and Applied Mathematics, 233 (2009), 730-738.
  41. Luis Garza, Francisco Marcellán, “Linear spectral transformations and Laurent polynomials”, Mediterranean Journal of Mathematics, 6 (2009) 273-289.
  42. Luis Garza, Francisco Marcellán, “Verblunsky parameters and linear spectral transformations”, Methods and Applications of Analysis, 16 (2009), 069-086.
  43. Luis Garza, Francisco Marcellán, “Szego transformations and Nth order associated polynomials on the unit circle”, Computers and Mathematics with Applications, 57 (2009), 659-671.
  44. 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.
  45. Luis Garza, Javier Hernández, Francisco Marcellán, "Spectral transformations of measures on the unit circle and the Szego transformation”, Numerical Algorithms, 49 (2008) 169-185.