Chromatic series with prolate spheroidal wave functions
Ignjatovic introduced the theory of chromatic derivatives in the technical report of the Kromos Corporation. Chromatic series are series expansions in which the coefficients are linear combinations of derivatives of a function. They were introduced as a replacement for Taylor's series and are based on orthogonal polynomials. Prolate spheroidal wave functions (PSWFs) arise as solution of an integral equation. This makes them band limited functions in a Paley-Wiener space, but because they are also solutions to a Sturm-Liouville problem, they behave very much like polynomials locally. Since the PSWFs are close to orthogonal polynomials they can be used to replace them in the Ignjatovic theory. It has been extended further to prolate spheroidal wavelet series that then combine chromatic series with sampling series. This leads to an over determined system which can use either local or global data to approximate the original function.
scientific article; zbMATH DE number 5306884
scientific article