Multivariate Hybrid Orthogonal Functions

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Date
2020-03-12MFO Scientific Program
Research in Pairs 2019Series
Oberwolfach Preprints;2020,04Author
Bracciali, Cleonice F.
Pérez, Teresa E.
Metadata
Show full item recordOWP-2020-04
Abstract
We consider multivariate orthogonal functions satisfying hybrid orthogonality conditions
with respect to a moment functional. This kind of orthogonality means that the product of
functions of different parity order is computed by means of the moment functional, and the product of elements of the same parity order is computed by a modification of the original moment functional.
Results about existence conditions, three term relations with matrix coefficients, a Favard type theorem for this kind of hybrid orthogonal functions are proved. In addition, a method to construct bivariate hybrid
orthogonal functions from univariate orthogonal polynomials and univariate orthogonal
functions is presented. Finally, we give a complete description of a sequence of hybrid orthogonal
functions on the unit disk on $\mathbb{R}^2$, that includes, as particular case, the classical orthogonal polynomials on the disk.