Overview
- Provides a concise introduction to linear functional analysis
- Presents results in the basic framework of a normed space and of an inner product space
- Includes a result by Zabreiko, which is used to deduce several major theorems in functional analysis
- Contains 160 exercises of various difficulty levels, and their solutions provided at the end of the book
- Will benefit senior undergraduate students in mathematics and graduate students in the natural sciences and engineering
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Table of contents (6 chapters)
Keywords
- Adjoint of a Bounded Linear Map
- Approximate Eigenspectrum
- Banach Space
- Bounded Inverse Theorem
- Bounded Linear Map
- Closed Graph Theorem
- Compact Linear Map
- Dual Space
- Eigenspectrum
- Hahn-Banach Theorems
- Hilbert Space
- Normal Operator
- Open Mapping Theorem
- Self-adjoint Operator
- Spectral Theory
- Spectrum of a Bounded Operator
- Transpose of a Bounded Linear Map
- Uniform Boundedness Principle
- Unitary Operator
- Zabreiko Theorem
About this book
The entire book can be used as a textbook for an introductory course in functional analysis without having to make any specific selection from the topics presented here. Basic notions in the setting of a metric space are defined interms of sequences. These include total boundedness, compactness, continuity and uniform continuity. Offering concise and to-the-point treatment of each topic in the framework of a normed space and of an inner product space, the book represents a valuable resource for advanced undergraduate students in mathematics, and will also appeal to graduate students and faculty in the natural sciences and engineering. The book is accessible to anyone who is familiar with linear algebra and real analysis.
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Authors and Affiliations
About the author
Professor Limaye earned his PhD in mathematics from the University of Rochester, New York, in 1969. His research interests include algebraic analysis, numerical functional analysis and linear algebra. He has published more than 50 articles inrefereed journals. In 1995, he was invited by the Indian Mathematical Society (IMS) to deliver the Sixth Srinivasa Ramanujan Memorial Award Lecture. In 1999 and in 2014, he received the “Award for Excellence in Teaching” from the IIT Bombay. An International Conference on “Topics in Functional Analysis and Numerical Analysis” was held in his honour in 2005, and its proceedings were published in a special issue of The Journal of Analysis in 2006. He is an emeritus member of the American Mathematical Society and a life member of the Indian Mathematical Society.
He is author/coauthor of several books: (i) Textbook of Mathematical Analysis (Tata McGraw-Hill, 1980), (ii) Functional Analysis (Wiley Eastern, 1981; New Age International, 1996), (iii) Spectral Perturbation and Approximation with Numerical Experiments (Australian National University, 1987), (iv) Real Function Algebras (Marcel Dekker, 1992), (v) Spectral Computations for Bounded Operators (CRC Press, 2001), (vi) A Course in Calculus and Real Analysis (Springer, 2006), and (vii) A Course in Multivariable Calculus and Analysis (Springer, 2010).
Bibliographic Information
Book Title: Linear Functional Analysis for Scientists and Engineers
Authors: Balmohan V. Limaye
DOI: https://doi.org/10.1007/978-981-10-0972-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media Singapore 2016
Hardcover ISBN: 978-981-10-0970-9Published: 24 June 2016
Softcover ISBN: 978-981-10-9298-5Published: 07 June 2018
eBook ISBN: 978-981-10-0972-3Published: 18 June 2016
Edition Number: 1
Number of Pages: XIV, 255
Number of Illustrations: 35 b/w illustrations, 1 illustrations in colour
Topics: Functional Analysis, Real Functions