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Linear Functional Analysis (Springer Undergraduate Mathematics Series)

Rynne, Bryan; Youngson, M.A.

1 ratings by Goodreads
ISBN 10: 1852332573 / ISBN 13: 9781852332570
Published by U.S.A.: Springer, 2006
Used Condition: As New Soft cover
From Pengwan Liu (Allen, TX, U.S.A.)

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Fast shipping from TX, Brand new, international edition, same content as US edition, soft cover, coverpage and ISBN may be different. Bookseller Inventory # ABE-1472767678938

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Bibliographic Details

Title: Linear Functional Analysis (Springer ...

Publisher: U.S.A.: Springer

Publication Date: 2006

Binding: Soft cover

Book Condition:As New

Edition: International Edition

About this title

Synopsis:

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.

Review:

"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

"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

"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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