Functions in R and C, including the theory of Fourier series,
Fourier integrals and part of that of holomorphic functions, form
the focal topic of these two volumes. Based on a course given by
the author to large audiences at Paris VII University for many
years, the exposition proceeds somewhat nonlinearly, blending
rigorous mathematics skilfully with didactical and historical
considerations. It sets out to illustrate the variety of possible
approaches to the main results, in order to initiate the reader to
methods, the underlying reasoning, and fundamental ideas. It is
suitable for both teaching and self-study. In his familiar,
personal style, the author emphasizes ideas over calculations and,
avoiding the condensed style frequently found in textbooks,
explains these ideas without parsimony of words. The French edition
in four volumes, published from 1998, has met with resounding
success: the first two volumes are now available in English.
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