Chromatic expansions of generalized functions

Abstract

Chromatic series expansions of bandlimited functions have recently been introduced as an alternative representation of the Whittaker–Shannon–Kotel'nikov sampling series. Chromatic series share similar properties with the Taylor series insofar as the coefficients of the expansions, which are called chromatic derivatives, are based on the ordinary derivatives of the function. The goal of this paper is to extend the notion of chromatic derivatives and series to spaces of generalized functions and obtain chromatic series for integral transforms of generalized functions, such as the Laplace, Fourier, and Hankel transforms.

Keywords:

• chromatic derivatives
• chromatic series
• bandlimited functions
• generalized functions
• integral transforms

1991 Mathematics Subject Classification :

• Primary: 44A15
• 41A58
• Secondary: 46F12
• 33C45
• 44A10