A First Course in Harmonic Analysis [Paperback]

Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition)

A primer in harmonic analysis on the undergraduate level

Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory.

Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology.

Almost all proofs are given in full and all central concepts are presented clearly.

Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula.

Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups.

Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

The second part of the book concludes with Plancherels theorem in Chapter 8. This theorem is a generalization of the completeness of the Fourier series, as well as of Plancherels theorem for the real line. The third part of the book is intended to provide the reader with a ?rst impression of the world of non-commutative harmonic analysis. Chapter 9 introduces methods that are used in the analysis of matrix groups, such as the theory of the exponential series and Lie algebras. These methods are then applied in Chapter 10 to arrive at a clas- ?cation of the representations of the group SU(2). In Chapter 11 we give the Peter-Weyl theorem, which generalizes the completeness of the Fourier series in the context of compact non-commutative groups and gives a decomposition of the regular representation as a direct sum of irreducibles. The tlÃF