**
Functional Analysis (2E) by Walter Rudin
**

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**About this book :- **
**Functional Analysis (2E) ** written by
** Walter Rudin **

In addition to Functional Analysis, Second Edition, Walter Rudin is the author of two other books: Principles of Mathematical Analysis and Real and Complex Analysis, whose widespread use is illustrated by the fact that they have been translated into a total of 13 languages. He wrote Principles of Mathematical Analysis while he was a C.L.E. Moore Instructor at the Massachusetts Institute of Technology—just two years after receiving his Ph.D. at Duke University. Later, he taught at the University of Rochester, and is now a Vilas Research Professor at the University of Wisconsin Madison. In the past, he has spent leaves at Yale University, the University of California in La Jolla, and the University of Hawaii. Dr. Rudin's research has dealt mainly with harmonic analysis and with complex variables. He has written three research monographs on these topics: Fourier Analysis on Groups, Function Theory in Polydiscs, and Function Theory in the Unit Ball ofCn.

Functional analysis is the study of certain topological-algebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems.

A good introductory text on this subject should include a presentation of its axiomatics (i.e., of the general theory of topological vector spaces), it should treat at least a few topics in some depth, and it should contain some interesting applications to other branches of mathematics. I hope that the present book meets these criteria.

The subject is huge and is growing rapidly. (The bibliography in volume I of [4] contains 96 pages and goes only to 1957.) In order to write a book of moderate size, it was therefore necessary to select certain areas and to ignore others. I fully realize that almost any expert who looks at the table of contents will find that some of his or her (and my) favorite topics are missing, but this seems unavoidable. It was not my intention to write an encyclopedic treatise. I wanted to write a book that would open the way to further exploration.

Part of the Student Series in Advanced Mathematics, this text is written for graduate courses in functional analysis. Used in modern investigations in analysis and applied mathematics, it includes Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.

**Book Detail :- **
** Title: ** Functional Analysis
** Edition: ** Second Edition
** Author(s): ** Walter Rudin
** Publisher: ** McGraw-Hill
** Series: **
** Year: ** 1991
** Pages: ** 443
** Type: ** PDF
** Language: ** English
** ISBN: ** 0070542368,9780070542365
** Country: ** US

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**About Author :- **

Author ** Walter Rudin ** (1921 – 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.

Rudin was known for his work on mathematical analysis, functional analysis, complex analysis and harmonic analysis. Rudin was also familiarly known to students as "Baby Rudin", "Papa Rudin", and "Grandpa Rudin"

He had obtain his Ph.D. from Duke University. He was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States.

**Book Contents :- **
**Functional Analysis (2E) ** written by
** Walter Rudin **
cover the following topics.
**Part I General Theory**

1. Topological Vector Spaces

2. Completeness

3. Convexity

4. Duality in Banach Spaces

5. Some Applications
**Part II Distributions and Fourier Transforms**

6. Test Functions and Distributions

7. Fourier Transforms

8. Applications to Differential Equations

9. Tauberian Theory
**Part III Banach Algebras and Spectral Theory**

10. Banach Algebras

11. Commutative Banach Algebras

12. Bounded Operators on a Hilbert Space

13. Unbounded Operators
**Appendix**

A Compactness and Continuity

B Notes and Comments

Bibliography

List of Special Symbols

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