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Generalized Hermite polynomials and the Bose-like oscillator calculus

Marvin Rosenblum
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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.

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Marvin Rosenblum. 1993-07-25. Generalized Hermite polynomials and the Bose-like oscillator calculus. https://arxiv.org/abs/math/9307224

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