This tract gives a clear exposition of the elementary theory of
Fourier transforms, so arranged as to give easy access to the
recently developed abstract theory of Fourier transforms on a
locally compact group. (This latter subject has important
applications to the general treatment of unitary representations of
the rotation group, the Lorentz group and other classical groups
that is of value in quantum field theory and other branches of
mathematical physics.) A knowledge of Lebesgue integration and, in
one chapter, of Riemann-Stieltjes integration is assumed; the
results needed are all stated in the introductory chapter.
General
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