This second edition has been enlarged and considerably rewritten.
Among the new topics are infinite product spaces with applications
to probability, disintegration of measures on product spaces,
positive definite functions on the line, and additional information
about Weyl's theorems on equidistribution. Topics that have
continued from the first edition include Minkowski's theorem,
measures with bounded powers, idempotent measures, spectral sets of
bounded functions and a theorem of Szego, and the Wiener Tauberian
theorem. Readers of the book should have studied the Lebesgue
integral, the elementary theory of analytic and harmonic functions,
and the basic theory of Banach spaces. The treatment is classical
and as simple as possible. This is an instructional book, not a
treatise. Mathematics students interested in analysis will find
here what they need to know about Fourier analysis. Physicists and
others can use the book as a reference for more advanced topics.
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