Krall--type Orthogonal Polynomials in several variables

2007/12/29 by Lidia Fernández, Fernandez, Lidia, Teresa E. Pérez +5 · 1 citation
Mathematics · Physics and Astronomy · #33C50 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.0801.0065

openalex publication_date 2007/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment functional. Explicit formula for the reproducing kernel is also derived and used to establish certain inequalities for classical orthogonal polynomials.

Cited by

• Bivariate multiple orthogonal polynomials of mixed type on the step-line

Related

• Bivariate multiple orthogonal polynomials of mixed type on the step-line
• -1 Krall-Jacobi Polynomials
• Orthogonal polynomials of several variables
• Orthogonal polynomials through the invariant theory of binary forms
• Orthogonal polynomials in several variables for measures with mass points