Fundamentals of Fourier Analysis

Loukas Grafakos

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Hardback

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English

Springer International Publishing AG
22 July 2024

Complex analysis, complex variables; Functional analysis & transforms

Series: Graduate Texts in Mathematics

This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit, each chapter presents a valuable selection of exercises with targeted hints that will assist the reader in the development of research skills. Proofs are presented with care and attention to detail. Examples are provided to enrich understanding and improve overall comprehension of the material. Carefully drawn illustrations build intuition in the proofs. Appendices contain background material for those that need to review key concepts. Compared with the author’s other GTM volumes (Classical Fourier Analysis and Modern Fourier Analysis), this text offers a more classroom-friendly approach as it contains shorter sections, more refined proofs, and a wider range of exercises. Topics include the Fourier Transform, Multipliers, Singular Integrals, Littlewood–Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, and can be easily covered within two semesters.

By: Loukas Grafakos
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2024 ed.
Volume: 302
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031564994
ISBN 10: 3031564995
Series: Graduate Texts in Mathematics
Pages: 407
Publication Date: 22 July 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Loukas Grafakos is the Mahala and Rose Houchins Distinguished Professor of Mathematics at the University of Missouri at Columbia. He is author of 3 Graduate Texts in Mathematics: Classical Fourier Analysis (GTM 249), Modern Fourier Analysis (GTM 250), and Fundamentals of Fourier Analysis (GTM 302). His research is in Harmonic Analysis.

Reviews for Fundamentals of Fourier Analysis

“The well-written monograph is intended to serve the purposes of a two-semester course. ... this textbook is very useful for graduate students in mathematics and a convenient reference for researchers working on multi-dimensional Fourier analysis.” (Manfred Tasche, zbMATH 1551.42001, 2025)