This book offers a complete and streamlined treatment of the
central principles of abelian harmonic analysis: Pontryagin
duality, the Plancherel theorem and the Poisson summation formula,
as well as their respective generalizations to non-abelian groups,
including the Selberg trace formula. The principles are then
applied to spectral analysis of Heisenberg manifolds and Riemann
surfaces. This new edition contains a new chapter on p-adic and
adelic groups, as well as a complementary section on direct and
projective limits. Many of the supporting proofs have been revised
and refined. The book is an excellent resource for graduate
students who wish to learn and understand harmonic analysis and for
researchers seeking to apply it.
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