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
Primo
2006-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.