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 Groups
  • Harmonic Analysis on Finite Abelian Groups
  • Set Theory and Topology
  • Invariant Means on Abelian Groups
  • Duality of Discrete and Compact Abelian Groups
  • Duality of Elementary Abelian Groups
  • Harmonic Analysis on Compact Abelian Groups
  • Duality of Locally Compact Abelian Groups
  • Haar Integral on Locally Compact Abelian Groups
  • Harmonic Analysis on Locally Compact Abelian Groups
• Spectral Analysis and Synthesis:
  • Basic Concepts
  • Basic Function Classes
  • The Torsion Free Rank
  • Spectral Analysis
  • Spectral Synthesis

Readership: Graduate students and researchers in the fields of harmonic analysis and functional analysis.