Introduction to Harmonic Analysis (Third Edition in English)

Author: Katznelson
Publisher:
Publish Date: 2005-01-01
Features: "This book achieves a perfect balance between concrete materials and abstract concepts. The author has a keen eye in selecting suitable topics. The clear and concise exposition of the subject matter, along with the numerous exercises provided, undoubtedly makes it an ideal knowledge source for those seeking to master the fundamentals of this discipline." — 2002 Steele Prize Citation This book has firmly established its classic status since its publication in 1968 and has been highly regarded by both students and experts. Professor Katznelson was awarded the Steele Prize in 2002 for this book. Starting with a clear exposition of classical Fourier analysis, the book aims to present the central ideas of harmonic analysis through a concrete framework and provides numerous examples to help readers gain a thorough understanding of the theory of harmonic analysis. After establishing these ideas, the author extends harmonic analysis far beyond the scope of circular groups and opens the door to other fields by discussing the Fourier transform on the real line and giving a brief examination of Fourier analysis on locally compact abelian groups. Compared to previous editions, this version includes additional supplementary material, including various topics in approximation theory and examples of applying probabilistic methods in harmonic analysis.