@misc{10481/72667,
year = {2021},
month = {10},
url = {http://hdl.handle.net/10481/72667},
abstract = {The so-called Koornwinder bivariate orthogonal polynomials
are generated by means of a non-trivial procedure involving two families
of univariate orthogonal polynomials and a function ρ(t) such that ρ(t)2
is a polynomial of degree less than or equal to 2. In this paper, we extend
the Koornwinder method to the case when one of the univariate families
is orthogonal with respect to a Sobolev inner product. Therefore, we
study the new Sobolev bivariate families obtaining relations between
the classical original Koornwinder polynomials and the Sobolev one,
deducing recursive methods in order to compute the coefficients. The
case when one of the univariate families is classical is analysed. Finally,
some useful examples are given.},
organization = {Ministerio de Ciencia, Innovación y
Universidades (MICINN) grant PGC2018-096504-B-C33},
organization = {EDER/Ministerio de Ciencia, Innovación
y Universidades—Agencia Estatal de Investigación/PGC2018-094932-B-I00},
organization = {Research Group FQM-384 by Junta de Andalucía},
organization = {IMAG-María de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033},
organization = {Universidad de Granada/CBUA},
publisher = {Springer Nature},
keywords = {Bivariate orthogonal polynomials},
keywords = {Sobolev orthogonal polynomials},
title = {Bivariate Koornwinder–Sobolev Orthogonal Polynomials},
doi = {10.1007/s00009-021-01875-6},
author = {Marriaga, Misael E. and Pérez Fernández, Teresa Encarnación and Piñar González, Miguel Ángel},
}