Manuel Domínguez de la Iglesia
Investigador Titular B
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Mailing address:
Circuito Exterior, C.U.,
04510 Ciudad de México, México.
Office: 220
Phone: (+52) 55 5622 4780
Fax: (+52) 55 5616 0348
E-mail: mdi29[at]im[dot]unam[dot]mx
Research interests
Approximation Theory, Special Functions, Orthogonal Polynomials, Matrix-valued Orthogonal Polynomials, Bispectral Problems, Matrix Analysis, Riemann-Hilbert problems, Fourier Analysis, Markov and stochastic processes, Quantum Markov chains.
Books:
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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.
Articles:
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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 (with 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 (with 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 (with 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 (with 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 (with F. A. Grünbaum and 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, 48-82 (with Esteban Tabak).
ArXiv
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Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials, Commun. Math. Phys. 326 (2014), 559-583 (with Mattia Cafasso).
ArXiv
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Differential equations for discrete Laguerre-Sobolev orthogonal polynomials,
J. Approx. Theory 195 (2015), 70-88 (with 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 (with A. J. Durán).
ArXiv
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Constructing Krall-Hahn orthogonal polynomials,
J. Math. Anal. Appl. 424 (2015), 361-384 (with A. J. Durán).
ArXiv
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Differential equations for discrete Jacobi-Sobolev orthogonal polynomials,
J. Spectral Theory 8 (2018), 191-234 (with A. J. Durán).
ArXiv
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Some bivariate stochastic models arising from group representation theory,
Stoch. Proc. Appl. 128 (2018), 3300-3326 (with 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 (with A. J. Durán).
ArXiv
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Stochastic LU factorizations, Darboux transformations and urn models,
J. Appl. Prob. 55 (2018), 862-886 (with 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 (with F. A. Grünbaum).
ArXiv
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Bispectral Laguerre type polynomials, Integral Transforms and Special Functions 31 (2020), 133-151(with 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. (with 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. (with 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. (with C. Juarez).
ArXiv
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Bispectral Jacobi type polynomials, Adv. Appl. Math. 136 (2022), 102322, 35 pp. (with A. J. Durán).
ArXiv
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An urn model for the Jacobi-Piñeiro polynomials, Proc. Amer. Math. Soc. 150 (2022), 3613-3625 (with 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 . (with 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. (with 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 (with C. Juarez).
ArXiv
Talks in conferences:
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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. September 1, 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). March 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), April 22, 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, Spain, September 18, 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, September 24-28, 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, Belgium, May 20, 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. Leganés, Madrid, September 8,
2008.
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Riemann-Hilbert techniques in the theory of orthogonal matrix polynomials.
XI Encuentros de Análisis Real y Complejo. Chinchón, Madrid, Spain, May 9,
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. March 9, 2010.
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Differential properties of orthogonal matrix polynomials.
International Congress of Mathematicians. Hyderabad, India. August 21, 2010.
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Differential properties of orthogonal matrix polynomials.
I Encuentro Nacional de Jóvenes Investigadores en Matemáticas. Sevilla, Spain. September 3, 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, February 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, September 1, 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. Liège, Belgium, Junio 7, 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, Denmark, June 12, 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, Spain, January, 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, Spain, February, 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, May 20-24, 2013.
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Constructing bispectral orthogonal polynomials from the classical families of Charlier, Meixner and Krawtchouk.
Constructive Functions 2014. Nashville, Tenneessee (USA), May 26-30, 2014.
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Differential equations for discrete Laguerre-Sobolev orthogonal polynomials.
IV Iberoamerican Workshop on Orthogonal Polynomials and Applications. Bogotá, Colombia, June 17-20, 2014.
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Aplicaciones de la ortogonalidad matricial a procesos estocásticos.
XLVII Congreso Nacional de la Sociedad Matemática Mexicana. Durango, México, October 26-31, 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 (USA), June 1-5, 2015.
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Krall-Hahn orthogonal polynomials.
Workshop on Orthogonal and Multiple Orthogonal Polynomials, BIRS-CMO, Oaxaca (México), August 9-14, 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), September 7-11, 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), June 5-10, 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, May 9-12, 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, July 3-7, 2017.
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Darboux transformations for quasi-birth-and-death processes.
VII Iberoamerican Workshop on Orthogonal Polynomials and Applications, Leganés, Madrid, July 3-6, 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, July 22-26, 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 México, September 2-6, 2019.
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Bispectrality of Laguerre and Jacobi type polynomials.
Operator Theory, Analysis and Mathematical Physics (OTAMP 2020), Ciudad de México, January 8-14, 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, México, June 14-18, 2021 (online).
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Stochastic factorizations of birth-death chains and Darboux transformations.
Mathematical Congress of the Americas, Buenos Aires, Argentina, July 12-23, 2021 (online).
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Discrete Krall polynomials.
Baylor Analysis Fest, Waco, TX, USA, May 24, 2022.
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Bispectral Jacobi type polynomials.
16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 16), Montreal, Canada, June 17, 2022 (online).
Seminars:
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Differential properties of some families of matrix valued
orthogonal polynomials and applications.
Courant Institute of
Mathematical Sciences. New York, March 11, 2008.
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Methods and applications of orthogonal matrix polynomials
satisfying differential equations.
Katholieke Universiteit Leuven. Leuven, June 11,2008.
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The Riemann-Hilbert problem for matrix-valued orthogonal polynomials.
Katholieke Universiteit Leuven. Leuven, November 5, 2008.
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Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization.
Université d'Angers. Angers, France, April 17, 2012.
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Estudio espectral de procesos estocásticos bidimensionales. Componentes principales dinámicas.
Universidad Tecnologica de Panamá, Panamá, September 4, 2012.
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Principal Dynamical Components.
Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brasil, May 15, 2013.
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Riemann-Hilbert characterization for matrix orthogonal polynomials.
City University of Hong Kong, China, May 28, 2013.
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Spectral methods for bivariate Markov processes.
City University of Hong Kong, China, May 30, 2013.
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Spectral methods for bivariate Markov processes.
Instituto de Matemáticas, UNAM, Sede CU, México, June 25, 2013.
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Spectral methods for bivariate Markov processes.
Instituto de Matemáticas, UNAM, Sede Cuernavaca, México, June 27, 2013.
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Como construir familias biespectrales de polinomios ortogonales a partir de familias clásicas.
Instituto de Matemáticas, UNAM, Sede CU, México, May 13, 2014.
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Aplicaciones de polinomios ortogonales matriciales.
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS), UNAM, México, January 15, 2015.
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Sobre algunas extensiones de polinomios ortogonales y sus aplicaciones.
Instituto de Matemáticas, UNAM, Sede Cuernavaca, México, January 21, 2015.
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Representación espectral de caminatas aleatorias.
CIMAT, Guanajuato, México, April 6, 2015.
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Polinomios ortogonales matriciales que verifican ecuaciones diferenciales.
Universidad Autónoma Metropolitana, Iztapalapa, Ciudad de México, February 25, 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, September 20, 2016.
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Teoría de la aproximación para funciones matriciales.
Instituto Tecnológico Autónomo de México, Ciudad de México, October 7, 2016.
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Algunas aplicaciones de polinomios ortogonales.
Universidad Autónoma de Aguascalientes, Aguascalientes, March 17, 2017.
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Nuevos métodos para el análisis espectral de caminatas aleatorias.
Universidad de Colima, Colima, November 17, 2017.
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Transformaciones de Darboux para caminatas aleatorias.
Centro de Ciencias Matemáticas, UNAM, Morelia, March 8, 2018.
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Biespectralidad de polinomios definidos mediante un determinante de tipo Casorati. II Escuela de Análisis Matemático, IMATE-UNAM, August 1, 2018.
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Historia y aplicaciones de polinomios ortogonales. Hablando de Matemáticas, IMATE-UNAM, March 21, 2019.
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Caminatas aleatorias y polinomios ortogonales. CINVESTAV, Ciudad de México, May 22, 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, August 13, 2019.
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Modelos de urnas para polinomios de tipo Jacobi. Seminario Grupo GOYA, Granada, Spain, May 28, 2021 (online).
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Historia y aplicaciones de polinomios ortogonales. Seminario Iberoamericano de Análisis Matemático y Matemática Aplicada, February 11, 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, May 15, 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, May, 2013.
PhD Thesis
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PhD Thesis: Propiedades diferenciales de familias de polinomios ortogonales
matriciales y aplicaciones. Reviewed version (July 2008).
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Defense (spanish). February 21, 2008.