On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis

  • A. A. Kalyuzhnyi
  • N. A. Kachanovskii


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.
How to Cite
Kalyuzhnyi, A. A., and N. A. Kachanovskii. “On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 7, July 2001, pp. 892-07, https://umj.imath.kiev.ua/index.php/umj/article/view/4311.
Research articles