Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
| Autor: | Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Algebra and Number Theory
Física-Modelos matemáticos Nonlinear Sciences - Exactly Solvable and Integrable Systems Multiple orthogonal polynomials FOS: Physical sciences Christofel Formulas Darboux transformations Oscillatory matrices Totally nonnegative matrices Mathematics - Classical Analysis and ODEs Favard spectral representation Classical Analysis and ODEs (math.CA) FOS: Mathematics Física matemática 42C05 33C45 33C47 Tetradiagonal Hessenberg matrices Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics Analysis |
| Popis: | Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pi\~neiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin. Comment: This is the third part of the splitting of the paper arXiv:2203.13578 into three. 15 pages and 1 figure |
| Databáze: | OpenAIRE |
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