1993/07/25 by Marvin Rosenblum, Rosenblum, Marvin · 2 citations
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Orbital Angular Momentum in Optics #Quantum Mechanics and Non-Hermitian Physics #math.CA
paper · pdf · doi:10.48550/arxiv.math/9307224
arxiv created 1993/07/25 · openalex publication_date 1993/07/25 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.