Harmonic and spectral analysis / by László Székelyhidi (University of Debrecen, Hungary).

Includes bibliographical references and index.

Print version record.

Abtract harmonic analysis. 1. Duality of finite Abelian groups -- 2. Harmonic analysis on finite Abelian -- 3. Set theory and topology -- 4. Invariant means on Abelian groups -- 5. Duality of discrete and compact Abelian groups -- 6. Duality of elementary Abelian groups -- 7. Harmonic analysis on compact Abelian groups -- 8. Duality of locally compact Abelian groups -- 9. Haar Integral on locally compact Abelian groups -- 10. Harmonic analysis on locally compact Abelian groups -- Spectral analysis and synthesis. 11. Basic concepts -- 12. Basic function classes -- 13. The torsion free rank -- 14. Spectral analysis -- 15. Spectral synthesis.

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.

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