IISGNII गुरुर ब्रह्मा गुरुर विष्णु गुरुर देवो महेश्वरः गुरुः साक्षात्परब्रह्मा तस्मै श्री गुरुवे नमः

FUNCTIONAL ANALYSIS : A FIRST COURSE-------PHI

350.00 332.00

Description:

Intended as an introductory-level text on Functional Analysis for the postgraduate students in Mathematics, this compact and well-organized text covers all the topics considered essential to the subject. In so doing, it provides a very good understanding of the subject to the reader.

The book begins with a review of linear algebra, and then it goes on to give the basic notion of a norm on linear space (proving thereby most of the basic results), progresses gradually, dealing with operators, and proves some of the basic theorems of Functional Analysis. Besides, the book analyzes more advanced topics like dual space considerations, compact operators, and spectral theory of Banach and Hilbert space operators.

The text is so organized that it strives, particularly in the last chapter, to apply and relate the basic theorems to problems which arise while solving operator equations.

• Plenty of examples have been worked out in detail, which not only illustrate a particular result, but also point towards its limitations so that subsequent stronger results follow.
• Exercises, which are meant to aid understanding and to promote mastery of the subject, are interspersed throughout the text.


This student friendly text, with its clear exposition of concepts, should prove to be a boon to the beginner aspiring to have an insight into Functional Analysis.

Contents:
Preface. Acknowledgements. Note to the Reader. Review of Linear Algebra. Normed Linear Spaces. Operators on Normed Linear Spaces. More about Hilbert Spaces. Hahn-Banach Theorem and Its Consequences. Uniform Boundedness Principle. Closed Graph Theorem and Its Consequences. Dual Space Consid-erations. Compact Operators. Spectral Results for Banach Space Operators. Operators on Hilbert Spaces. Spectral Results for Hilbert Space Operators. Spectral Representations. Solution of Operator Equations. References. Index.  

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