Discrete Spectral Synthesis and Its Applications (Springer Monographs in Mathematics) - Hardcover

Székelyhidi, László

Hardcover

ISBN 10: 1402046367 ISBN 13: 9781402046360

Publisher: Springer, 2006

Synopsis

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.

About this title

Synopsis

Spectral analysis and spectral synthesis deal with the description of translation invariant function spaces over locally compact Abelian groups. Translation invariant function spaces appear in several different contexts for example linear ordinary and partial difference and differential equations with constant coefficients, theory of group representations, classical theory of functional equations. A fundamental problem is to discover the structure of such spaces of functions, or more exactly, to find an appropriate class of basic functions, the building blocks, which serve as "typical elements" of the space, a kind of basis. It turns out that these building blocks are the exponential monomials. The problem of spectral analysis is if the function spaces in question contain any exponential monomials. However, the problem of spectral synthesis is in ascertaining if there are enough exponential monomials in these function spaces to span a dense subspace.

This book studies the situation over discrete Abelian groups with wide range applications in the fields of classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups.

Edition details

• Publisher: Springer
• Publication date: 2006
• Language: English
• ISBN 10: 1402046367
• ISBN 13: 9781402046360
• Binding: Hardcover
• Number of pages: 134