Some examples of matrix-valued orthogonal functions having a\n differential and an integral operator as eigenfunctions

2010/06/04 by Manuel D. de la Iglesia, de la Iglesia, Manuel D.
Computer Science · Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Optical and Acousto-Optic Technologies

paper · pdf · doi:10.48550/arxiv.1006.0962

openalex publication_date 2010/06/04 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to show some examples of matrix-valued orthogonal\nfunctions on the real line which are simultaneously eigenfunctions of a\nsecond-order differential operator of Schr "odinger type and an integral\noperator of Fourier type. As a consequence we derive integral representations\nof these functions as well as other useful structural formulas. Some of these\nfunctions are plotted to show the relationship with the Hermite or wave\nfunctions.\n

Citations

• Random walks and orthogonal polynomials: some challenges

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