On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis - Kalyuzhnyi, A. A.; Kachanovskii, N. A. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{λ + λ }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{λ } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$ 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.