Overview

Providing an introduction to the ideas and methods of linear functional analysis, this book shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. In the initial chapters, the theory of infinite-dimensional normed spaces (in particular Hilbert spaces) is developed, while in later chapters the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapter discusses the two particularly important areas of integral and differential equations. The reader is assumed to have a standard undergraduate knowledge of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration. An introductory chapter summarizes the requisite material. Many exercises are included with solutions provided for each.

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9781852332570

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The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having gotten somewhere worth getting by a sensibly paced, clearly signposted route. Mathematical Gazette, 2000 <p> It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations. CHOICE magazine <p> The presentation is quite elementary, and there are sufficiently many illuminating examples and exercises??? this nice textbook perfectly fits the readership, i.e., undergraduate students in mathematics and physics??? It may be recommended to all students who want to get in touch with the basic ideas of functional analysis and operator theory for the first time. Zentralblatt MATH

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