The aim of this paper is the study of some transformations in the
Laguerre-Hahn affine class that do not preserve the class. Under very
general conditions, we establish that the second kind functional
associated with a Laguerre-Hahn affine functional does not belong to
the Laguerre-Hahn affine class. The transformations related to the
associated polynomials and quadratic decomposition of a sequence of
orthogonal polynomials are also considered.
Publié le : 2003-01-14
Classification:
Orthogonal polynomials,
Laguerre-Hahn affine linear functionals,
second degree functionals,
second kind functionals,
33C47,
42C05
@article{1047309419,
author = {Cachafeiro, A. and Marcell\'an, F. and P\'erez, C.},
title = {Second kind functionals for the
Laguerre-Hahn affine class on the unit circle},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {10},
number = {1},
year = {2003},
pages = { 125-140},
language = {en},
url = {http://dml.mathdoc.fr/item/1047309419}
}
Cachafeiro, A.; Marcellán, F.; Pérez, C. Second kind functionals for the
Laguerre-Hahn affine class on the unit circle. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp. 125-140. http://gdmltest.u-ga.fr/item/1047309419/