Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory.
Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible.
The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.

A unique development of a field by seven founding authors, together with reproductions of some of their basic papers Applications to dyadic differential equations, approximation theory, etc Reviews of former and recent results help the reader to get a fast introduction and a rather complete coverage of the area. A separate chapter with open problems should be useful for further research in the field Includes supplementary material: sn.pub/extras

Inhalt
Early Work in Gibbs Differentiation in China.- Gibbs-Butzer Calculus and Pseudo-differential Operators on Local Fields.- Early Work in Gibbs Differentiation in Soviet Union SSSR.- Research in Dyadic Differentiation in Russia.- Generalized Derivatives and Integrals on Vilenkin Groups.- Calculus on Walsh and Vilenkin Groups.- Gibbs Derivatives on Groups.- My Research in Gibbs Derivatives on Finite Groups.- Efcient Computation of Gibbs Derivatives on Finite Abelian Groups.- Gibbs Derivative and Walsh Harmonizable DSP.- My Involvement in Gibbs Derivatives and Walsh Harmonizable Processes.- Open Problems in Theory and Applications of Dyadic Derivatives.