Generalized Hermite Polynomials and the Bose-Like Oscillator Calculus

  • Marvin Rosenblum
Part of the Operator Theory: Advances and Applications book series (OT, volume 73)


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.


Entire Function Selfadjoint Operator Confluent Hypergeometric Function Riesz Theorem Rodrigues Formula 
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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Marvin Rosenblum
    • 1
  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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