CURRICULUM VITAE: ANTONIO J. DURAN

CURRICULUM VITAE: ANTONIO J. DURAN
(updated: December, 2015)
1. Personal data.
Name: Antonio J. Durán
Date of birth: April 25, 1962
Office address: Departamento de Análisis Matemático; Facultad de Matemáticas;
Universidad de Sevilla; Apart. (P.O. Box) 1160; 41080 Sevilla; Spain
Phone: 34 95 455 7980 Fax: 34 95 455 7972
E. Mail: duran@us.es
2. Academic qualifications.
Ph. D. in Mathematics (1988). Universidad de Sevilla
3. Employment.
Full professor since 1996 in the Universidad de Sevilla
4. Publications
Journals
Around 80 papers published in International Journals, 53 of which in Q1 (according to Web of Science 2013) with 732 citations by 244 authors (according
to MathSciNet/Mathematical Reviews).
1. The Stieltjes moments problem for rapidly decreasing functions, Proceedings of the American Mathematical Society, 107, 731–741, 1989.
2. Laguerre expansions of tempered distributions and generalized functions,
Journal of Mathematical Analysis and Applications, 150, 166–180, 1990.
3. On Hankel transform Proceedings of the American Mathematical Society,
110, 417–424, 1990.
4. with J. Arias de Reyna; Some results about the space A−∞ of analytic
functions, Michigan Mathematical Journal, 37, 339–345, 1990.
5. A bound on the Laguerre polynomials, Studia Mathematica, 100, 169–
181, 1991.
6. The analytic functionals in the lower half plane as a Gelfand-Shilov space,
Mathematische Nachrichten, 153, 145–167, 1991.
7. Gelfand-Shilov spaces for the Hankel transform, Indagationes Mathematicae, 3, 137–151, 1992.
8. The Stieltjes moment problem with complex exponents, Mathematische
Nachrichten, 158, 175–194, 1992.
9. Functions with given moments and weight functions for orthogonal polynomials, Rocky Mountain Journal of Mathematics, 23, 87–104, 1993.
1
10. A generalization of Favard’s Theorem for polynomials satisfying a recurrence relation, Journal of Approximation Theory, 74, 83–104, 1993.
11. Laguerre expansions in Gelfand-Shilov spaces, Journal of Approximation
Theory, 74, 280–300, 1993.
12. On orthogonal polynomials with respect to a positive definite matrix of
measures, Canadian Journal of Mathematics, 47, 88–112, 1995.
13. with W. Van Assche; Orthogonal matrix polynomials and higher order
recurrence relations Linear Algebra and Applications 219,261–280,1995.
14. with C. Berg; The index of determinacy for measures and the `2 norm
of orthonormal polynomials, Transactions of the American Mathematical
Society, 347, 2795–2811, 1995.
15. with P. López-Rodrı́guez; Orthogonal matrix polynomials: zeros and Blumenthal’s theorem, Journal of Approximation Theory, 84, 96–118, 1996.
16. When does a discrete differential perturbation of a sequence of orthonormal polynomials belong to `2 ?, Journal of Functional Analysis, 136, 127–
153, 1996.
17. Markov’s theorem for orthogonal matrix polynomials, Canadian Journal
of Mathematics, 48, 1180–1195, 1996.
18. with C. Berg; Orthogonal polynomials, L2 spaces and entire functions,
Mathematica Scandinavica, 79, 209–223, 1996.
19. Matrix inner product having a matrix symmetric second order differential
operator, Rocky Mountain Journal of Mathematics, 27, 585–600, 1997.
20. with C. Berg, Measures with finite index of determinacy or a mathematical model for Dr. Jekyll and Mr. Hyde, Proceedings of the American
Mathematical Society, 125, 523–530, 1997.
21. The Hausdorff moment problem with complex exponents and a MuntzSzasz theorem for distributions, Mathematische Nachrichten, 187, 79–99,
1997.
22. Ratio asymptotics and quadrature formula, Constructive Approximation,
13, 271–286, 1997.
23. with P. López-Rodrı́guez; The Lp space of a positive definite matrix of
measures and density of matrix polynomials in L1 , Journal of Approximation Theory, 90, 299–318, 1997.
24. with P. López-Rodrı́guez; Density questions for the truncated matrix
moment problem, Canadian Journal of Mathematics , 49, 708–721, 1997.
2
25. Ratio asymptotic for orthogonal matrix polynomials, Journal of Approximation Theory, 100, 304–344, 1999.
26. with P. López-Rodrı́guez and E. Saff; Zero asymptotic behaviour for
orthogonal matrix polynomials, Journal d’analyse Mathematique, 78, 37–
60, 1999.
27. with P. López-Rodrı́guez: N-Extremal matrices of measures for an indeterminate matrix moment problem, Journal of Functional Analysis, 174,
301-321, 2000.
28. with E. Daneri; Ratio asymptotics for orthogonal matrix polynomiasl
with unbounded recurrence coefficients, Journal of Approximation Theory,
110, 1–17, 2001.
29. with E. Defez, Orthogonal matrix polynomials and quadrature formulae,
Linear Algebra and Applications, 345, 71–84, 2002.
30. with E. Saff; Zero location for non-standard orthogonal polynomials,
Journal of Approximation Theory, 113, 127–141, 2001.
31. with E. Daneri; Weak asymptotics for orthogonal matrix polynomials,
Indagationes mathematicae, 13, 47–62, 2002.
32. with B. Polo; Gauss quadrature formulae for orthogonal matrix polynomials Linear Algebra and Applications, 355, 119–146, 2002.
33. with M. Castro; Boundedness properties for Sobolev inner products, Journal of Approximation Theory, 122, 97–111, 2003.
34. with B. Polo; Matrix Christoffel functions, Constructive Approximation ,
20, 353–376, 2004.
35. with C. Berg; A transformation from Hausdorff to Stieltjes moment sequences, Arkiv Mathematik, 42, 239–257, 2004.
36. with F. A. Grunbaum; Orthogonal matrix polynomials satisfying second
order differential equations, International Mathematical Research Notices,
10, 461–484, 2004.
37. with F. A. Grunbaum; Orthogonal matrix polynomials, scalar type Rodrigues’ formulas and Pearson equations, Journal of Approximation Theory, 134, 267–280, 2005.
38. with F. A. Grunbaum; A survey on orthogonal matrix polynomials satisfying second order differential equations, Journal of Computational and
Applied Mathematics, 178, 169–190, 2005.
39. with F. A. Grunbaum; A characterization for a class of weight matrices
with orthogonal matrix polynomials satisfying second order differential
equations, International Mathematical Research Notices, 23, 1371–1390,
2005.
3
40. with F. A. Grunbaum: Structural formulas for orthogonal matrix polynomials satisfying second order differential equations I, Constructive Approximation, 22, 255–271, 2005.
41. with C. Berg; Some transformation of the Hausdorff moment problems
and harmonic numbers, Canadian Journal of Mathematics, 57, 941–960,
2005.
42. with C. Berg, Analytic functions associated to positive definite infinite
matrices, Journal of Mathematical Analysis and Applications, 315, 54–67,
2006.
43. with M.E.H. Ismail; Differential coefficients of orthogonal Matrix Polynomials, Journal of Computational and Applied Mathematics, 190, 424–436,
2006.
44. with F. A. Grunbaum; P.A.M. Dirac meets M.G. Krein: matrix orthogonal
polynomials and Dirac’s equation, Journal of Physics A, 39, 3655–3662,
2006.
45. with Pedro López Rodrı́guez; Structural formulas for orthogonal matrix
polynomials satisfying second order differential equations II, Constructive
Approximation, 26, 29–47, 2007.
46. with F. A. Grunbaum; Matrix orthogonal polynomials satisfying second
order differential equations: coping without help from group representation theory, Journal of Approximation Theory, 148, 35–48, 2007.
47. C. Berg; The fix point for a transformation of Hausdorff moment sequences and iteration of a rational functions, Mathematica Scandinavica,
103, 11–39, 2008.
48. with M. Domı́nguez de la Iglesia; Some examples of orthogonal matrix
polynomials satisfying odd order differential equations, Journal of Approximation Theory, 150, 153–174 2008.
49. with C. Berg, Iteration of the rational function z − 1/z and a Hausdorff
moment sequence, Expositiones Mathematicae, 26, 375–385, 2008.
50. with M. Domı́nguez de la Iglesia; Second order differential operators having several families of orthogonal polynomials as eigenfunctions, International Mathematical Research Notices, –, 2008
51. Generating orthogonal matrix polynomials satisfying second order differential equations from a trio of triangular matrices, Journal of Approximation Theory, 161, 88–113, 2009.
52. A method to find weight matrices having symmetric second order differential operators with matrix leading coefficient, Constructive Approximation, 29, 181–206, 2009.
4
53. with F. A. Grunbaum; Matrix differential equations and scalar polynomials satisfying higher order recursions, Journal of Mathematical Analysis
and Applications, 354, 1–11, 2009.
54. Rodrigues’ formulas for orthogonal matrix polynomials satisfying second
order differential equations, International Mathematical Research Notices,
–2009.
55. Rodrigues’ formulas for orthogonal matrix polynomials satisfying higher
order differential equations, Experimental Mathematics, 20, 15–24, 2011.
56. with C. Berg; Fibonacci numbers, Euler two periodic continuous fractions
and moment sequences, The Fibonacci Quarterly, 49, 66–75, 2011.
57. A miraculously commuting family of orthogonal matrix polynomials satisfying second order differential equations, Journal of Approximation Theory, 163, 1815–1833, 2011.
58. with Jorge Borrego y Mirta Castro; Orthogonal matrix polynomials satisfying differential equations with recurrence coefficients having non-scalar
limits, Integral transform and special functions, 23, 685–700, 2012.
59. Orthogonal polynomials satisfying higher order difference equations, Constructive Approximation, 36, 459–486, 2012.
60. The algebra of difference operators associated to a family of orthogonal
polynomials, Journal of Approximation Theory, 164, 586–610, 2012.
61. with Nikta Shayanfar; Constructing orthogonal matrix polynomials satisfying differential equations from two different Laguerre weights, Integral
transforms and special functions, 24, 263–279, 2013.
62. with R. Álvarez-Nodarse y A. Martı́nez de los Rı́os; Orthogonal matrix
polynomials satisfying second order difference equations, Journal of Approximation Theory, 169, 40–55, 2013.
63. Using D-operators to construct orthogonal polynomials satisfying higher
order difference or differential equations, Journal of Approximation Theory, 174, 10–53, 2013.
64. Symmetries for Casorati determinants of classical discrete orthogonal polynomials, Proceedings of the American Mathematical Society, 142, 915–
930, 2014.
65. with V. Sánchez Canales; Orthogonal matrix polynomials whose differences are also orthogonal, Journal of Approximation Theory, 179, 112–
127, 2014.
66. with A. Martı́nez de los Rı́os; The convex cone of weight matrices associated to a second order matrix difference operator, Integral Transform and
Special Function,–2014.
5
67. Exceptional Charlier and Hermite orthogonal polynomials, Journal of Approximation Theory, 182, 29–58, 2014.
68. Exceptional Meixner and Laguerre orthogonal polynomials, Journal of Approximation Theory, 184, 176–208, 2014.
69. with Sánchez Canales; Rodrigues’ Formulas for Orthogonal Matrix Polynomials Satisfying Second-Order Difference Equations, Integral Transform
and Special Function, 25, 849–863, 2014.
70. with M. Pérez Riera y J.L. Varona; The misfortunes of a trio of mathematicians using Computer Algebra Systems. Can we trust in them?,
Notices of the American Mathematical Society, 611249–12522014.
71. Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities Journal of Combinatorial Theory A,
124, 57–96, 2014.
72. with R. Álvarez Nodarse; Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations, Journal of Mathematical Analysis and Applications, 424, 304–320, 2015.
73. with M. Domı́nguez de la Iglesia; Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk,
Constructive Approximation, 41, 49–91, 2015.
74. with M. Domı́nguez de la Iglesia; Constructing Krall-Hahn orthogonal
polynomials, Journal of Mathematical Analysis and Applications, 424,
361–384, 2015.
75. with M. Pérez Riera; Admissibility condition for exceptional Laguerre
polynomials, Journal of Mathematical Analysis and Applications, 424,
1042–1053, 2015.
76. with M. Domı́nguez de la Iglesia; Differential equations for discrete LaguerreSobolev orthogonal polynomials, Journal of Approximation Theory, 195,
70–88, 2015.
77. Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials Integral Transforms and Special Functions, 26, 357–376,2015
78. with M. Pérez Riera y J.L. Varona; Some conjectures on Wronskian and
Casorati determinants of orthogonal polynomials, Experimental Mathematics, 24, 123–132, 2015.
79. Constructing bispectral dual Hahn polynomials, Journal of Approximation
Theory, , –, 2015.
80. with Jorge Arvesú Casorati type determinants of some q-classical polynomials Proceedings of the American Mathematical Society, , –, 2015.
6
Books
Long and recognized expertise in promoting public awareness and understanding
of mathematics (outreach). Over a dozen of books published on history of
mathematics and to promote mathematics for general audience, among which
my favorite are:
1. Historia, con personajes, de los conceptos del cálculo, Alianza Editorial,
Madrid, 1996.
2. Introducción al análisis de los infinitos (de L. Euler), Real Sociedad Matemática
Española y SAEM Thales, Sevilla, 2001.
3. Análisis de cantidades mediante series, fluxiones y diferencias (de I. Newton), Real Sociedad Matemática Española y SAEM Thales, Sevilla, 2003.
4. Vida de los números, T-ediciones, Madrid, 2006.
5. Obras escogidas de Arquı́medes, Real Sociedad Matemática Española,
Patrimonio Nacional e ICM-2006, Sevilla, 2006.
6. Isaac Newton y Gottfried Leibniz: La polémica sobre la invención del
cálculo infinitesimal, Crı́tica, Barcelona, 2006
7. Pasiones, piojos, dioses... y matemáticas, Destino, Barcelona, 2009.
8. La poesı́a de los números, RBA, Barcelona, 2010.
9. El ojo de Shiva, el sueño de Mahoma, Simbad... y los números, Destino,
Barcelona, 2012.
10. El universo sobre nosotros, Crı́tica, Barcelona, 2015.
Some of these books have been translated to English, French, Italian, Polish,
Portuguese and Russian.
5. International meetings and lectures
1. Organizer or member of the Scientific Committee of more than 10 International meetings.
2. Participation in 70 international meetings and conferences.
3. 60 Lectures in 40 Universities along the world..
6. Ph. D. Students
1. Pedro López-Rodrı́guez, 1995.
2. Mirta Castro-Smirnova, 2002.
3. Beatriz Polo, 2002.
7
4. Enrique Daneri, 2003.
5. Manuel Domı́nguez de la Iglesia, 2008.
6. Ana Martı́nez de los Rı́os, 2014.
7. Vanesa Sánchez Canales, 2014.
7. Other Research related activity
1. Editor in Chief of the Real Sociedad Matemática Española (2002-2005).
2. President of the Organizing Committee of the VIII Simposium on orthogonal polynomials and their applications: International meeting held at the
Universidad de Sevilla in September 1997.
3. Member of the Scientific Committee for the First Joint meeting American
Mathematical Society and Real Sociedad Matemática Española, Sevilla in
June 2003.
4. Member of the Executive Committee for the International Congress of
Mathematicians, Madrid, 2006.
5. Member of the Executive Committee for Ingenio Mathematica, Consolider
Project, 2006-2012.
6. Investigator in charge or member of more than 20 research projects.
7. Curator of two important expositions: El legado de las matemáticas: de
Euclides a Newton, los genios a través de sus libros, (Mathematic’s legacy:
from Euclid to Newtwon, genius through their books), Reales Alcázares
de Sevilla, from December 2000 to January 2001 (50.000 visitors in three
weeks); and Vida de los números (The life of numbers), Biblioteca Nacional
en Madrid, from June to September, 2006.
8