Manuel Domínguez de la Iglesia
Investigador Titular B
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Dirección postal:
Circuito Exterior, C.U.,
04510 Ciudad de México, México.
Cubículo: 220
Teléfono: (+52) 55 5622 4780
Fax: (+52) 55 5616 0348
E-mail: mdi29[at]im[dot]unam[dot]mx
Líneas de investigación
Teoría de Aproximación, funciones especiales, polinomios ortogonales, polinomios ortogonales matriciales, problemas biespectrales, análisis matricial, problemas de Riemann-Hilbert, análisis de Fourier, procesos de Markov y estocásticos, cadenas de Markov cuánticas.
Libros:
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Orthogonal polynomials in the spectral analysis of Markov processes. Birth-death models and diffusion, Encyclopedia of Mathematics and its Applications 181, Cambridge University Press, 2022.
Artículos:
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Matrix valued orthogonal polynomials related to SU(N+1),
their algebras of differential operators and the corresponding
curves, Exp. Math. 16, No. 2, (2007), 189-207 (con F. A. Grünbaum).
.
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Some examples of orthogonal matrix polynomials satisfying
odd order differential equations, J. Approx. Theory 150, No. 2, (2008), 153-174 (con A. J. Durán).
.
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Matrix valued orthogonal polynomials arising from group
representation theory and a family of quasi-birth-and-death
processes, SIAM J. Matrix Anal. Applic. 30, No. 2 (2008), 741-761 (con F. A. Grünbaum).
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Second order differential operators having several families
of orthogonal matrix polynomials as eigenfunctions, Internat. Math. Research Notices, Vol. 2008, Article ID rnn084, 24
pages (con A. J. Durán).
ArXiv
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A note on the invariant distribution of a quasi-birth-and-death process,
J. Phys. A: Math. Theor. 44 (2011) 135201 (9pp).
ArXiv
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Some examples of matrix-valued orthogonal functions having a differential and an integral
operator as eigenfunctions,
J. Approx. Theory 163, No. 5, (2011), 663--687.
ArXiv
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Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization,
SIGMA 7 (2011), 098, 31 pages (con F. A. Grünbaum y A. Martínez-Finkelshtein).
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Spectral methods for bivariate Markov processes with diffusion and discrete components and a variant of the Wright-Fisher model,
J. Math. Anal. Appl. 393 (2012), 239-255.
ArXiv
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Principal dynamical components, Comm. Pure Appl. Math. 66 (2013), no. 1, 4882 (con Esteban Tabak).
ArXiv
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Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials, Commun. Math. Phys. 326 (2014), 559-583 (con Mattia Cafasso).
ArXiv
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Differential equations for discrete Laguerre-Sobolev orthogonal polynomials,
J. Approx. Theory 195 (2015), 70-88 (con A. J. Durán).
ArXiv
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Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk,
Constr. Approx. 41 (2015), 49-91 (con A. J. Durán).
ArXiv
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Constructing Krall-Hahn orthogonal polynomials,
J. Math. Anal. Appl. 424 (2015), 361-384 (con A. J. Durán).
ArXiv
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Differential equations for discrete Jacobi-Sobolev orthogonal polynomials,
J. Spectral Theory 8 (2018), 191-234 (con A. J. Durán).
ArXiv
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Some bivariate stochastic models arising from group representation theory,
Stoch. Proc. Appl. 128 (2018), 3300-3326 (con Pablo Román).
ArXiv
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The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre type, SIGMA 14 (2018), 076, 17 pages (con M. Cafasso).
ArXiv
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On difference operators for symmetric Krall-Hahn polynomials, Integral Transforms and Special Functions 29 (2018), 699-718 (con A. J. Durán).
ArXiv
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Stochastic LU factorizations, Darboux transformations and urn models,
J. Appl. Prob. 55 (2018), 862-886 (con F. A. Grünbaum).
ArXiv
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Stochastic Darboux transformations for quasi-birth-and-death processes and urn models, J. Math. Anal. Appl. 478 (2019), 634-654 (con F. A. Grünbaum).
ArXiv
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Bispectral Laguerre type polynomials, Integral Transforms and Special Functions 31 (2020), 133-151(con A. J. Durán).
ArXiv
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The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers, J. Approx. Theory 258 (2020) 105458, 32 pp. (con C. Juarez).
ArXiv
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Quasi-birth-and-death processes and multivariate orthogonal polynomials, J. Math. Anal. Appl. 499 (2021), 125029, 33 pp. (con L. Fernández).
ArXiv
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Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformations, J. Approx. Theory 266 (2021) 105583, 27 pp. (con C. Juarez).
ArXiv
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Bispectral Jacobi type polynomials, Adv. Appl. Math. 136 (2022), 102322, 35 pp. (con A. J. Durán).
ArXiv
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An urn model for the Jacobi-Piñeiro polynomials, Proc. Amer. Math. Soc. 150 (2022), 3613-3625 (con F. A. Grünbaum).
ArXiv
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Spectral analysis of bilateral birth-death processes: some new explicit examples, Adv. Appl. Prob. 54 (2022), 1193-1221.
ArXiv
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Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics, Quantum Inf Process 22 (2023), 60, 57 pp . (con C. Lardizabal and N. Loebens).
ArXiv
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Birth-death chains on a spider: spectral analysis and reflecting-absorbing factorization, J. Math. Anal. Appl. 517 (2023), 126624, 20 pp. (con C. Juarez).
ArXiv
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QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models, Mediterr. J. Math. 20 (2023), no.6, Paper No. 290, 23 pp. (with L. Fernández).
ArXiv
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The bilateral birth-death chain generated by the associated Jacobi polynomials, Stud. Appl. Math. 151 (2023) 616-642 (con C. Juarez).
ArXiv
Charlas en congresos:
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Matrix valued orthogonal polynomials related to SU(N+1),
their algebras of differential operators and the corresponding
curves. Recent trends in Contructive Approximation Theory. Universidad Carlos III de Madrid. 1 de Septiembre de 2006.
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Some examples of orthogonal matrix polynomials satisfying odd order differential equations
. 12th International Conference in Approximation Theory. San Antonio, Texas (USA). Marzo 4-6, 2007.
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New phenomena on examples of orthogonal matrix polynomials satisfying differential equations
. 2007 AMS Spring Western Section Meeting. Tucson, Arizona (USA), 22 de Abril, 2007.
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Second order differential operators having several families
of orthogonal matrix polynomials as eigenfunctions.
Special Functions, Information Theory and Mathematical Physics. Granada, España, 18 de Septiembre, 2007.
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Matrix valued orthogonal polynomials satisfying differential equations.
XX Congreso de Ecuaciones Diferenciales y Aplicaciones. X Congreso de Matemática Aplicada. Sevilla, 24-28 Septiembre, 2007
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The convex cone of weight matrices associated with a symmetric
second order differential operator: some examples.
Workshop on
orthogonal polynomials and special functions. Katholieke
Universiteit Leuven. Leuven, 20 de Mayo, 2008.
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A family of quasi-birth-and-death processes coming from the
theory of matrix valued orthogonal polynomials.
International
workshop on orthogonal polynomials and approximation theory.
Universidad Carlos III de Madrid. Leganes, Madrid, 8 de Septiembre,
2008.
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Riemann-Hilbert techniques in the theory of orthogonal matrix polynomials.
XI Encuentros de Analisis Real y Complejo. Chinchon, Madrid, 9 de Mayo,
2009.
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Methods and new phenomena of orthogonal matrix polynomials satisfying differential equations.
13th International Conference in Approximation Theory. San Antonio, Texas. 9 de Marzo, 2010.
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Differential properties of orthogonal matrix polynomials.
International Congress of Mathematicians. Hyderabad, India. 21 de Agosto, 2010.
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Differential properties of orthogonal matrix polynomials.
I Encuentro Nacional de Jóvenes Investigadores en Matemáticas. Universidad de Sevilla. 3 de Septiembre, 2010.
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Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions.
Congreso de la Real Sociedad Matemática Española 2011. ávila, Febrero 1-5, 2011.
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Bivariate Markov processes and matrix orthogonality.
11th International Symposium on Orthogonal Polynomials,
Special Functions and Applications. Universidad Carlos III de Madrid, 1 de septiembre de 2011
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A variant of the Wright-Fisher diffusion model coming from the theory of matrix-valued spherical functions.
1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies. Lieja, Bélgica, 7 de junio de 2012
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Algebraic aspects of the Riemann-Hilbert problem for matrix orthogonal polynomials.
Orthogonal Polynomials and Special Functions: a Complex Analytic Perspective. Copenhague, Dinamarca, 12 de junio de 2012
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Integral equations and representations of some Hermite-type families of orthogonal matrix polynomials.
Congreso de la Real Sociedad Matemática Española 2013. Santiago de Compostela, España, enero de 2013.
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Integral representations of some Hermite type matrix-valued kernels and non-commutative Painlevé equations.
Primer Encuentro de la Red de Polinomios Ortogonales y Teoría de Aproximación ORTHONET 2013. Logroño, España, Febrero de 2013.
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Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials.
International Conference on Approximation Theory and Applications. Hong Kong, China, 20-24 de mayo de 2013.
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Constructing bispectral orthogonal polynomials from the classical families of Charlier, Meixner and Krawtchouk.
Constructive Functions 2014. Nashville, Tenneessee, EE.UU., 26-30 de mayo, 2014.
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Differential equations for discrete Laguerre-Sobolev orthogonal polynomials.
IV Iberoamerican Workshop on Orthogonal Polynomials and Applications. Bogotá, Colombia, 17-20 de junio, 2014.
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Aplicaciones de la ortogonalidad matricial a procesos estocásticos.
XLVII Congreso Nacional de la Sociedad Matemática Mexicana. Durango, México, 26-31 de octubre, 2014.
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Differential equations for discrete Sobolev orthogonal polynomials.
13th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-13), National Institute of Standards and Technology, Gaithersburg, Maryland (EE.UU.), 1-5 de junio, 2015.
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Krall-Hahn orthogonal polynomials.
Workshop on Orthogonal and Multiple Orthogonal Polynomials, BIRS-CMO, Oaxaca (México), 9-14 de agosto, 2015.
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Approximation of matrix functions via orthogonal matrix polynomials.
First Joint International Meeting of the Israel Mathematical Union and the Mexican Mathematical Society, Oaxaca (México), 7-11 de septiembre, 2015.
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Two stochastic models related with an example coming from group representation theory.
XII International Conference in Approximation and Optimization in the Caribbean, Universidad de La Habana (Cuba), 5-10 de junio, 2016.
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Some recent developments about birth-and-death models and orthogonal polynomials.
VI Iberoamerican Workshop on Orthogonal Polynomials and Applications, Uberaba, 9-12 de mayo de 2017.
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Factorization of stochastic Jacobi matrices into two stochastic factors and Darboux transformations.
14th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 14), Canterbury, 3-7 de julio de 2017.
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Darboux transformations for quasi-birth-and-death processes.
VII Iberoamerican Workshop on Orthogonal Polynomials and Applications, Leganés, Madrid, 3-6 de julio de 2018.
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Bispectral Laguerre and Jacobi type polynomials.
15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 15), Hagenberg, Austria, 22-26 de julio de 2019.
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The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers. Bath-UNAM-CIMAT Meeting XVI (BUC XVI), Ciudad de Mexico, 2-6 septiembre de 2019.
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Bispectrality of Laguerre and Jacobi type polynomials.
Operator Theory, Analysis and Mathematical Physics (OTAMP 2020), Ciudad de Mexico, 8-14 de enero de 2020.
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Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformation.
V Encuentro Conjunto de la Real Sociedad Matemática Española (RSME) y la Sociedad Matemática Mexicana (SMM), Guanajuato, Mexico, 14-18 Junio, 2021 (online).
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Stochastic factorizations of birth-death chains and Darboux transformations.
Mathematical Congress of the Americas, Buenos Aires, Argentina, 12-23 Julio, 2021 (online).
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Discrete Krall polynomials.
Baylor Analysis Fest, Waco, TX, USA, 24 de mayo de 2022.
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Bispectral Jacobi type polynomials.
16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 16), Montreal, Canada, 17 de junio de 2022 (online).
Seminarios:
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Differential properties of some families of matrix valued
orthogonal polynomials and applications.
Courant Institute of
Mathematical Sciences. New York, 11 de marzo, 2008.
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Methods and applications of orthogonal matrix polynomials
satisfying differential equations.
Katholieke Universiteit Leuven. Leuven, 11 de junio,2008.
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The Riemann-Hilbert problem for matrix-valued orthogonal polynomials.
Katholieke Universiteit Leuven. Leuven, 5 de noviembre, 2008.
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Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization.
Université d'Angers. Angers, France, 17 de abril, 2012.
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Estudio espectral de procesos estocásticos bidimensionales. Componentes principales dinámicas.
Universidad Tecnologica de Panamá, Panamá, 4 de septiembre, 2012.
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Principal Dynamical Components.
Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brasil, 15 de mayo, 2013.
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Riemann-Hilbert characterization for matrix orthogonal polynomials.
City University of Hong Kong, China, 28 de mayo, 2013.
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Spectral methods for bivariate Markov processes.
City University of Hong Kong, China, 30 de mayo, 2013.
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Spectral methods for bivariate Markov processes.
Instituto de Matemáticas, UNAM, Sede CU, México, 25 de junio, 2013.
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Spectral methods for bivariate Markov processes.
Instituto de Matemáticas, UNAM, Sede Cuernavaca, México, 27 de junio, 2013.
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Como construir familias biespectrales de polinomios ortogonales a partir de familias clásicas.
Instituto de Matemáticas, UNAM, Sede CU, México, 13 de mayo, 2014.
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Aplicaciones de polinomios ortogonales matriciales.
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS), UNAM, México, 15 de enero, 2015.
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Sobre algunas extensiones de polinomios ortogonales y sus aplicaciones.
Instituto de Matemáticas, UNAM, Sede Cuernavaca, México, 21 de enero, 2015.
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Representación espectral de caminatas aleatorias.
CIMAT, Guanajuato, México, 6 de Abril de 2015.
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Polinomios ortogonales matriciales que verifican ecuaciones diferenciales.
Universidad Autónoma Metropolitana, Iztapalapa, Ciudad de México, 25 de febrero, 2016.
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Algunos ejemplos de análisis espectral de procesos de Markov bidimensionales.
Seminario de Probabilidad y Procesos Estocásticos, IMATE, UNAM, Ciudad de México, 20 de septiembre, 2016.
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Teoría de la aproximación para funciones matriciales.
Instituto Tecnológico Autónomo de México, Ciudad de México, 7 de octubre, 2016.
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Algunas aplicaciones de polinomios ortogonales.
Universidad Autónoma de Aguascalientes, Aguascalientes, 17 de marzo de 2017.
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Nuevos métodos para el análisis espectral de caminatas aleatorias.
Universidad de Colima, Colima, 17 de noviembre de 017.
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Transformaciones de Darboux para caminatas aleatorias.
Centro de Ciencias Matemáticas, UNAM, Morelia, 8 de marzo de2018.
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Biespectralidad de polinomios definidos mediante un determinante de tipo Casorati. II Escuela de Análisis Matemático, IMATE-UNAM, 1 de agosto de 2018.
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Historia y aplicaciones de polinomios ortogonales. Hablando de Matemáticas, IMATE-UNAM, 21 de marzo de 2019.
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Caminatas aleatorias y polinomios ortogonales. CINVESTAV, Ciudad de México, 22 de mayo de 2019.
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Matrices espectrales asociadas a transformaciones de Darboux estocásticas de caminatas aleatorias en los enteros. Coloquio del Instituto de Matemáticas, UNAM, Sede CU, México, 13 de agosto de 2019.
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Modelos de urnas para polinomios de tipo Jacobi. Seminario Grupo GOYA, Granada, España, 28 de mayo de 2021 (online).
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Historia y aplicaciones de polinomios ortogonales. Seminario Iberoamericano de Análisis Matemático y Matemática Aplicada, 11 de febrero de 2022 (online).
Posters:
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A family of quasi-birth-and-death processes coming from the
theory of matrix valued orthogonal polynomials.
3emes
Journees Approximation. Universite de Lille 1. Lille, 15 de mayo de 2008.
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A variant of the Wright-Fisher diffusion model coming from the thoery of matrix-valued spherical functions.
III Iberoamerican Workshop on Orthogonal Polynomials and Applications. Sao José do Rio Preto, Brasil, Mayo de 2013.
Tesis doctoral
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Tesis doctoral: Propiedades diferenciales de familias de polinomios ortogonales
matriciales y aplicaciones. Versión revisada (Julio 2008).
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Defensa de la tesis doctoral. 21 de febrero de 2008.