On zernicke transforms in spaces of distributions

Abstract

In this paper polynomials of two variables orthogonal on the unit disc with weight introduced by F. Zernicke and T. Koornwinder are considered. They are kernels of a discrete integral transformation in certain spaces of test functions and their duals. The operational calculus of this transformation is derived.

Keywords:

• disc polynomials
• complete orthogonal systems
• test functions
• gerneralized functions
• convolution structure

MSC(1991):

• 33C30
• 44A15
• 46F12