Orthogonal polynomials with respect to differential operators and matrix orthogonal polynomials

• Grant number: 12/21042-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2013
• End date: March 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alagacone Sri Ranga
• Grantee: Jorge Alberto Borrego Morell
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 09/13832-9 - Orthogonal polynomials, special functions and applications, AP.TEM

Abstract

In this project we pretend to work mainly in two themes: orthogonal polynomials with respect to a differential operator and matrix orthogonal polynomials. The problems associated to these themes that we will be treating have risen from the research results of my PhD thesis. In the first theme, we shall focus in questions of existence and uniqueness of orthogonal polynomials with respect to a differential operator, electrostatic models, zero location and asymptotic properties. This kind of orthogonality is relatively new and many questions are still open. In the second theme we propose to work with matrix orthogonal polynomials, specifically with those families of polynomials which satisfy a second order differential equation and Rodrigues' formulas. This theme is related to the Bochner matrix problem, which is still unsolved.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BORREGO-MORELL, J.; RANGA, A. SRI. Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, v. 28, n. 1, p. 39-55, JAN 2016. (12/21042-0, 09/13832-9)

BORREGO-MORELL, J.; RAFAELI, FERNANDO RODRIGO. On a class of biorthogonal polynomials on the unit circle. Journal of Mathematical Analysis and Applications, v. 438, n. 1, p. 465-473, JUN 1 2016. (12/21042-0)

BORREGO-MORELL, J.; RAFAELI, F. R.. An asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle. Applied Mathematics and Computation, v. 313, p. 52-73, NOV 15 2017. (12/21042-0)

BORREGO-MORELL, J.; PIJEIRA-CABRERA, H.. Differential orthogonality: Laguerre and Hermite cases with applications. Journal of Approximation Theory, v. 196, p. 111-130, AUG 2015. (12/21042-0)