Giorgio Mantica, Sandro Vaienti
The Asymptotic Behaviour of the Fourier
Transforms of Orthogonal Polynomials I: Mellin transform
techniques
(88K, latex)
ABSTRACT. The Fourier transforms 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 role of Mellin transform(s) techniques in deriving
classical and new results is underlined.