Harmonic And Spectral Analysis

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.
Contents:Abstract Harmonic Analysis:Duality of Finite Abelian GroupsHarmonic Analysis on Finite Abelian GroupsSet Theory and TopologyInvariant Means on Abelian GroupsDuality of Discrete and Compact Abelian GroupsDuality of Elementary Abelian GroupsHarmonic Analysis on Compact Abelian GroupsDuality of Locally Compact Abelian GroupsHaar Integral on Locally Compact Abelian GroupsHarmonic Analysis on Locally Compact Abelian GroupsSpectral Analysis and Synthesis:Basic ConceptsBasic Function ClassesThe Torsion Free RankSpectral AnalysisSpectral Synthesis
Readership: Graduate students and researchers in the fields of harmonic analysis and functional analysis.