We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the order, and in certain combinations of the two is required to solve a number of problems arising in quantum mechanics. We present known results, new approaches and open conjectures, hoping to justify our belief that the importance of these investigations extends beyond the application just mentioned, and may involve interesting discoveries.

Fourier-Bessel functions and the many asymptotics of orthogonal polynomials of singular continuous measures

MANTICA, GIORGIO DOMENICO PIO
2006

Abstract

We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the order, and in certain combinations of the two is required to solve a number of problems arising in quantum mechanics. We present known results, new approaches and open conjectures, hoping to justify our belief that the importance of these investigations extends beyond the application just mentioned, and may involve interesting discoveries.
Singular measures; Fourier transform; orthogonal polynomials; almost periodic Jacobi matrices; Fourier-Bessel functions; quantum intermittency; Julia sets; iterated function systems; generalized dimensions; potential theory.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/1500939
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