Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials

Spectral and factorization properties of oscillatory matrices lead to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials with respect to a set positive Lebesgue–Stieltjes measures. A mi...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) Vol. 434; p. 109313
Main Authors: Branquinho, Amílcar, Foulquié-Moreno, Ana, Mañas, Manuel
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2023
Subjects:
Bounded banded matrices
Favard spectral representation
Mixed multiple Gaussian quadrature
Mixed multiple orthogonal polynomials
Oscillatory matrices
Totally nonnegative matrices
33C47
Bounded banded matrices
Mixed multiple Gaussian quadrature
33C45
Totally nonnegative matrices
47B39
47B36
Favard spectral representation
Mixed multiple orthogonal polynomials
Oscillatory matrices
42C05
ISSN:0001-8708, 1090-2082
Online Access:Get full text
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Summary:Spectral and factorization properties of oscillatory matrices lead to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials with respect to a set positive Lebesgue–Stieltjes measures. A mixed multiple Gauss quadrature formula with corresponding degrees of precision is given.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109313