The primary goal of this text is to present the theoretical foundation
of the field of Fourier analysis. This book is mainly addressed to
graduate students in mathematics and is designed to serve for a
three-course sequence on the subject. The only prerequisite for
understanding the text is satisfactory completion of a course in measure
theory, Lebesgue integration, and complex variables. This book is
intended to present the selected topics in some depth and stimulate
further study. Although the emphasis falls on real variable methods in
Euclidean spaces, a chapter is devoted to the fundamentals of analysis
on the torus. This material is included for historical reasons, as the
genesis of Fourier analysis can be found in trigonometric expansions of
periodic functions in several variables.Download
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