The Fourier transform of orthogonal polynomials with respect to their own orthogonality measure defines the family of Fourier-Bessel functions. We study the asymptotic behaviour of these functions and of their products, for large real values of the argument. By employing a Mellin analysis we construct a general framework to exhibit the relation of the asymptotic decay laws to certain dimensions of the orthogonality measure, that are defined via the divergence abscissas of suitable integrals. The unifying r^ole of Mellin transform techniques in deriving classical and new results is underlined.

The asymptotic behaviour of the Fourier transform of orthogonal polynomials I: Mellin transform techniques

MANTICA, GIORGIO DOMENICO PIO;
2007-01-01

Abstract

The Fourier transform of orthogonal polynomials with respect to their own orthogonality measure defines the family of Fourier-Bessel functions. We study the asymptotic behaviour of these functions and of their products, for large real values of the argument. By employing a Mellin analysis we construct a general framework to exhibit the relation of the asymptotic decay laws to certain dimensions of the orthogonality measure, that are defined via the divergence abscissas of suitable integrals. The unifying r^ole of Mellin transform techniques in deriving classical and new results is underlined.
singular measures; Fourier transform; dimensions; orthogonal polynomials
Mantica, GIORGIO DOMENICO PIO; Vaienti, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1681321
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