**
Functional Analysis:Introduction to Further Topics in Analysis by Elias M. Stein, Rami Shakarchi
**

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**About this book :- **
**Functional Analysis:Introduction to Further Topics in Analysis ** written by
** Elias M. Stein, Rami Shakarchi **

While there are a number of excellent texts dealing with individual parts of what we cover, our exposition aims at a different goal: presentinig the various sub-areas of analysis not as separate disciplines, but rather as highly interconnected. It is our view that seeing these relations and their resulting synergies will motivate the reader to attain a better understanding of the subject as a whole. With this outcome in mind, we have concentrated on the main ideas and theorems that have shaped the field (sometimes sacrificing a more systematic approach), and we have been sensitive to the historical order in which the logic of the subject developed.

(Elias M. Stein)

**Book Detail :- **
** Title: ** Functional Analysis:Introduction to Further Topics in Analysis
** Edition: **
** Author(s): ** Elias M. Stein, Rami Shakarchi
** Publisher: ** World Scientific
** Series: **
** Year: ** 2011
** Pages: ** 442
** Type: ** PDF
** Language: ** English
** ISBN: ** 9780691113876, 9781400840557
** Country: ** US

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**About Author :- **

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.

**Book Contents :- **
**Functional Analysis:Introduction to Further Topics in Analysis ** written by
** Elias M. Stein, Rami Shakarchi **
cover the following topics.

1. Spaces and Banach Spaces

2. U Spaces in Harmonic Analysis

3. Distributions: Generalized Functions

4. Applications of the Baire Category Theorem

5. Rudiments of Probability Theory

6. An Introduction to Brownian Motion

7. A Glimpse into Several Complex Variables

8. Oscillatory Integrals in Fourier Analysis

9. Exercises

10. Problems

Notes and References

Bibliography

Symbol Glossary

Index

?1

?2

- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis

- Basic Algebra
- Basic Mathematics
- Math History
- Math Formulas
- Mathematical Methods
- Number Theory
- Bio Mathematics
- Business Mathematics
- Probability & Statistics