Generalized Hermite polynomials and the Bose-like oscillator calculus
Classical Analysis and ODEs
2016-09-06 v1
Abstract
This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator calculus, which generalizes the calculus associated with the quantum mechanical simple harmonic oscillator, is studied in terms of these polynomials.
Cite
@article{arxiv.math/9307224,
title = {Generalized Hermite polynomials and the Bose-like oscillator calculus},
author = {Marvin Rosenblum},
journal= {arXiv preprint arXiv:math/9307224},
year = {2016}
}