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Real and Functional Analysis by Gerald Teschl
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**About this book :- **
**Real and Functional Analysis ** written by
** Gerald Teschl **

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: ** Real and Functional Analysis
** Edition: **
** Author(s): ** Gerald Teschl
** Publisher: **
** Series: **
** Year: ** 2010
** Pages: ** 398
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: ** Austria

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**About Author :- **

Author ** Gerald Teschl ** (born 1970 in Graz) is an Austrian mathematical physicist and professor of mathematics. He works in the area of mathematical physics in particular direct and inverse spectral theory with application to completely integrable partial differential equations (soliton equations). He compelte his PhD in mathematics at the University of Missouri in 1995, thesis was Spectral Theory for Jacobi Operators and postdoctoral position at the Rheinisch-Westfälischen Technische Hochschule Aachen in 1996/97.

Since 1997 he has been a professor of mathematics at University of Vienna. In 1997 he received the Ludwig Boltzmann Prize from the Austrian Physical Society, 1999 the Prize of the Austrian Mathematical Society. In 2006 he was awarded with the prestigious START-Preis by the Austrian Science Fund (FWF). In 2011 he became a member of the Austrian Academy of Sciences (ÖAW).

His important research works are Sturm–Liouville theory, Jacobi operators and the Toda lattice. His most important contributions are to the fields of Sturm–Liouville theory, Jacobi operators and the Toda lattice. He also works in biomathematics, in particular in the novel area of breath gas analysis. He has written a successful undergraduate textbook (Mathematics for Computer Science, in German) with his wife Susanne Teschl.

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** • Download PDF Ordinary Differential Equations & Dynamical Systems by Gerald Teschl **

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**Book Contents :- **
**Real and Functional Analysis ** written by
** Gerald Teschl **
cover the following topics.
**Part-1 Functional Analysis**

1. A first look at Banach and Hilbert spaces

2. Hilbert spaces

3. Compact operators

4. The main theorems about Banach spaces

5. Further topics on Banach spaces

6. Bounded linear operators

7. Operator semigroups
**Part-2 Real Analysis**

8. Measures

9. Integration

10. The Lebesgue spaces Lp

11. More measure theory

12. The dual of Lp

13. Sobolev spaces

14. The Fourier transform

15. Interpolation
**Part-3 Nonlinear Functional Analysis**

17. The Brouwer mapping degree

18. The Leray–Schauder mapping degree

19. Monotone maps

Appendix A. Some set theory

Appendix B. Metric and topological spaces

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