. C A ] 2 5 Ju l 1 99 3 will GENERALIZED HERMITE POLYNOMIALS AND THE BOSE - LIKE OSCILLATOR CALCULUS
نویسنده
چکیده
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.
منابع مشابه
. C A ] 9 J ul 1 99 3 Jacobi polynomials of type BC , Jack polynomials , limit transitions and O ( ∞ )
2. A representation of O(∞). Since p ( 1 2 d− 3 2 , 1 2 d− 3 2 ) n has an interpretation as spherical function on O(d)/O(d− 1), the above limit formulas suggest that monomials and Hermite polynomials have some interpretation on O(∞). This is indeed the case, see for instance McKean [5] and Matsushima e.a. [4]. Let us explain this briefly. Let S be the sphere of radius (d/2) 1 2 and midpoint 0 i...
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