Chromatic Derivatives, Chromatic Expansions and Associated Spaces

This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess the best features of both the Taylor and the Shannon expansions. This makes chromatic derivatives and chromatic expansions applicable in fields involving empirically sampled data, such as digital signal and image processing. The first section of this paper is a 2 page extended abstract.