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fourier analysis and its applications, gerald folland [pdf]

Fourier Analysis: An Introduction by Elias M. Stein, Rami Shakarchi

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Fourier Analysis: An Introduction written by Elias M. Stein, Rami Shakarchi
The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
(Elias M. Stein, Rami Shakarchi)

Book Detail :-
Title: Fourier Analysis: An Introduction
Edition:
Author(s): Elias M. Stein, Rami Shakarchi
Publisher: Princeton University Press
Series: Princeton lectures in analysis
Year: 2003
Pages: 326
Type: PDF
Language: English
ISBN: 069111384X,9780691113845
Country: US

Author Elias Menachem Stein was an American mathematician who was famous because of his work in the field of harmonic analysis. He was professor of Mathematics at Princeton University from 1963 until his death in 2018.
Author Menachem Stein was born in Antwerp Belgium, to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium. In 1940, the Stein family move to the United States. He graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, before moving on to the University of Chicago for college. In 1955, Stein earned a Ph.D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.
Stein worked primarily in the field of harmonic analysis, and made contributions in both extending and clarifying Calderón–Zygmund theory. These include Stein interpolation, the Stein maximal principle, Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space and the space of functions of bounded mean oscillation.

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Book Contents :-
Fourier Analysis: An Introduction written by Elias M. Stein, Rami Shakarchi cover the following topics.
Foreword
Preface
1. The Genesis of Fourier Analysis
2. Basic Properties of Fourier Series
3. Convergence of Fourier Series
4. Some Applications of Fourier Series
5. The Fourier Transform on R
6. The Fourier Transform on Rd
7. Finite Fourier Analysis
8. Dirichlet's Theorem
Appendix: Integration
Notes and References
Bibliography
Symbol Glossary
Index

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