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On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis

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Abstract

We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function

$$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$

in the model one-dimensional case. The main results are a detailed intrinsic description of spaces of test functions, a description of generalized translation operators, and the investigation of integral C- and S-transformations.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. A. Kalyuzhnyi & N. A. Kachanovskii

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  1. A. A. Kalyuzhnyi
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  2. N. A. Kachanovskii
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Kalyuzhnyi, A.A., Kachanovskii, N.A. On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis. Ukrainian Mathematical Journal 53, 1061–1078 (2001). https://doi.org/10.1023/A:1013321030412

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