@misc{10481/108397,
year = {2026},
month = {3},
url = {https://hdl.handle.net/10481/108397},
abstract = {Classical generalized bivariate polynomials are families of bivariate symmetric
polynomials pγ
n,k(x, y) orthogonal with respect to the weight function
Wγ(x, y) = ω(x)ω(y)|x − y|
2γ+1, x, y ∈ (a, b),
where γ > −1, and ω(t) is one of the classical weight functions (Hermite, Laguerre,
Jacobi) on the real line. They are eigenfunctions of Dγ
1 , a second order partial
differential with rational coefficients. We consider raising or lowering operators for
these polynomials, that is, we study differential operators acting on orthogonal
polynomials to raise or lower their degree while preserving their orthogonality but
shifting the parameters in the weight function. The change of variables u = x+y, v =
xy allows us to construct a family of orthogonal polynomials by means of the identity
qγ
n,k(u, v) = pγ
n,k(x, y), those polynomials are eigenfunctions of partial differential
operators with polynomial coefficients and order 2 and 4 constructed from Dγ
1 and
the ladder operators. Finally, we show that these two operators generate the algebra
of differential operators that admit the polynomials qγ
n,k(u, v) as eigenfunctions.},
publisher = {Elsevier},
keywords = {Multivariate orthogonal polynomials},
keywords = {Symmetric polynomials},
keywords = {Classical generalized bivariate polynomials},
title = {Ladder operators for bivariate generalized classical symmetric orthogonal polynomials},
doi = {10.1016/j.jmaa.2025.130207},
author = {Alhama, Gema and Marriaga, Misael E. and Piñar González, Miguel Ángel},
}