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 11 - 2aλ + λ ^2 ( x 12_0^λ du u - 2au^2 + u^3 ),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.