Mellin transform theory and the role of its differential and integral operators

Abstract

The purpose of this overview paper is to present an approach to Mellin transform theory that is fully independent of Laplace or Fourier transform results, in a unified systematic form, one that contains the transform properties and results under natural, minimal assumptions upon the functions in question. Cornerstones are two definitions of the Mellin transform, a local and a global transform, the Mellin inversion theory, established by approximation theoretical methods connected with the Mellin convolution singular integral of Gauss-Weierstrass-type, and especially the Mellin operators of differentiation and anti-differentiation. (orig.)Available from TIB Hannover: RN 2414(468) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman