Mixed orthogonality on the unit ball

Author(s)

Bracciali, Cleonice F. ^[1] ; Perez, Teresa E. ^{[2, 3]}

Affiliation

^[1] UNESP Univ Estadual Paulista, Dept Matemat, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Granada, Fac Ciencias, Inst Matemat IEMath GR, Granada 18071 - Spain

^[3] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Granada 18071 - Spain

• Document type: Journal article
• Source: COMPUTATIONAL & APPLIED MATHEMATICS; v. 40, n. 8 DEC 2021.
• Web of Science Citations: 0

Abstract

We consider multivariate functions satisfying mixed orthogonality conditions with respect to a given 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. Three term relations and a Favard type theorem for this kind of mixed orthogonal functions are proved. In addition, a method to construct bivariate mixed orthogonal functions from univariate orthogonal polynomials and univariate mixed orthogonal functions is presented. Finally, we give a complete description of a sequence of mixed orthogonal functions on the unit disk on R-2, that includes, as a particular case, the classical orthogonal polynomials on the disk. (AU)

• FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
• Grantee: Dimitar Kolev Dimitrov
• Support Opportunities: Research Projects - Thematic Grants