2019
Том 71
№ 6

All Issues

On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis

Kachanovskii N. A., Kalyuzhnyi A. A.

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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.

English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 7, pp 1061-1078.

Citation Example: Kachanovskii N. A., Kalyuzhnyi A. A. On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis // Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 892-907.

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