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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
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Druck auf Anfrage Neuware - Printed after ordering - This book provides an introduction to the ideas and methods of linear fu- tional analysis at a level appropriate to the nal year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the t- ory of metric spaces). Part of the development of functional analysis can be traced to attempts to nd a suitable framework in which to discuss di erential and integral equations. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions de ned on some set. In general, such a v- tor space is in nite-dimensional. This leads to di culties in that, although many of the elementary properties of nite-dimensional vector spaces hold in in nite-dimensional vector spaces, many others do not. For example, in general in nite-dimensionalvectorspacesthereisnoframeworkinwhichtomakesense of analytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now brie y outline the contents of the book.…
Seller Inventory # 9781848000049
- Title
- Linear Functional Analysis
- Author
- Bryan Rynne
- Publisher
- Springer
- Publication year
- 2007
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 1848000049
- ISBN 13
- 9781848000049
- Edition
- 2nd Edition
- Item weight
- 586 grams
- Dimensions
- 235x178x19 mm
- Series
- Book 13 of 90: Springer Undergraduate Mathematics
"Synopsis" may belong to another edition of this title.
From the Back Cover
This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material.
The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.
Further highlights of the second edition include:
a new chapter on the Hahn–Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis;
extended coverage of the uniform boundedness theorem;
plenty of exercises, with solutions provided at the back of the book.
Praise for the first edition:
"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
"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
"About the title" may belong to another edition of this title.
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