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.

This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations.In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations.In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis.

The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate "marriage" where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods - and, sometimes, a new world of unexpected difficulties.

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.