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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Dedicated to Moshe Livšic
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Rosenblum, M. (1994). Generalized Hermite Polynomials and the Bose-Like Oscillator Calculus. In: Feintuch, A., Gohberg, I. (eds) Nonselfadjoint Operators and Related Topics. Operator Theory: Advances and Applications, vol 73. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8522-5_15
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DOI: https://doi.org/10.1007/978-3-0348-8522-5_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9663-4
Online ISBN: 978-3-0348-8522-5
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