Banded matrices and their orthogonality

2023/07/16 by Amílcar Branquinho, Branquinho, Amílcar, Ana Foulquié‐Moreno +3
Computer Science · Mathematics · Physics and Astronomy · #33C45 #33C47 #42C05 #60Gxx #60J10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Optical and Acousto-Optic Technologies #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2307.08081

openalex publication_date 2023/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the oscillatory character the Favard theorem for Jacobi matrices is revisited and it is shown that after an adequate shift of the Jacobi matrix one gets an oscillatory matrix. In this work we present a spectral theorem for this type of operators and show how the theory of multiple orthogonal polynomials apply.

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