Fundamentals of Fourier Analysis

Loukas Grafakos (Autor)

Buch | Softcover

XVI, 407 Seiten

2025
Springer International Publishing (Verlag)
978-3-031-56502-1 (ISBN)

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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.

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.

1 Introductory Material.- 2 Fourier Transforms, Tempered Distributions, Approximate Identities.- 3 Singular Integrals.- 4 Vector-Valued Singular Integrals and Littlewood-Paley Theory.- 5 Fractional Integrability or Differentiability and Multiplier Theorems.- 6 Bounded Mean Oscillation.- 7 Hardy Spaces.- 8 Weighted Inequalities.- Historical Notes.- Appendix A Orthogonal Matrices.- Appendix B Subharmonic Functions.- Appendix C Poisson Kernel on the Unit Strip.- Appendix D Density for Subadditive Operators.- Appendix E Transposes and Adjoints of Linear Operators.- Appendix F Faa di Bruno Formula.- Appendix G Besicovitch Covering Lemma.- Glossary.- References.- Index.

This book provides an introduction to Fourier analysis on Euclidean spaces intended for students who have completed first-year graduate courses in real and complex analysis. The text is self-contained and complete with numerous exercises in each section and seven appendices. (Cody B. Stockdale, Mathematical Reviews, May, 2025)

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)

Erscheinungsdatum	07.11.2025
Reihe/Serie	Graduate Texts in Mathematics
Zusatzinfo	XVI, 407 p. 29 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	639 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	bounded mean oscillation • Convolution and approximate identities • Fourier analysis textbook • Fractional integrability • Hardy Spaces • Harmonic analysis textbook • Interpolation • Littlewood-Paley theory • Maximal functions • Singular Integrals • weighted inequalities
ISBN-10	3-031-56502-9 / 3031565029
ISBN-13	978-3-031-56502-1 / 9783031565021
Zustand	Neuware