This book studies the situation over discrete Abelian groups with wide range applications. It covers classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups, giving unified treatment of several different problems. There is no other comprehensive work in this field. The book will be of interest to graduate students, research workers in harmonic analysis, spectral analysis, functional equations and hypergroups.

Zusammenfassung

In order to study discrete Abelian groups with wide range applications, the use of classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups is required. This book covers several different problems in this field and is unique in being the only comprehensive coverage of this topic. It should appeal to graduate students and researchers in harmonic analysis, spectral analysis, functional equations and hypergroups.

Inhalt
Spectral synthesis and spectral analysis.- Spectral analysis and spectral synthesis on discrete Abelian groups.- Spectral synthesis and functional equations.- Mean periodic functions.- Difference equations in several variables.- Spectral analysis and synthesis on polynomial hypergroups in a single variable.- Spectral analysis and synthesis on multivariate polynomial hypergroups.