- Paperback: 254 pages
- Publisher: Cambridge University Press (21 July 1988)
- Language English
- ISBN-10: 0521337178
- ISBN-13: 978-0521337175
- Product Dimensions: 22.6 x 15.1 x 1.4 cm
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Amazon Bestsellers Rank:
444,474 in Books (See Top 100 in Books)
- #3 in Books > Science & Nature > Mathematics > Transformations
- #33 in Books > Science & Nature > Mathematics > Algebra > Abstract
- See Complete Table of Contents
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Review
' … the author's style is a delight. Each topic is carefully motivated and succinctly presented, and the exposition is enthusiastic and limpid … Young has done a really fine job in presenting a subject of great mathematical elegance as well as genuine utility, and I recommend it heartily.' Times Higher Education Supplement
Product Description
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
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First Sentence
Some important metric notions such as length, angle and the energy of physical systems can be expressed in terms of the inner product (x,y) of vectors x, yEC. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Some important metric notions such as length, angle and the energy of physical systems can be expressed in terms of the inner product (x,y) of vectors x, yEC. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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6 reviews
14 of 14 people found the following review helpful
A Tantalizing Introduction to Hilbert Space
27 Feb 2002
Format:Paperback
Young has done an admirable job at presenting some really beautiful and useful aspects of Hilbert spaces in a manner comprehendable for advanced undergraduates. After reading the book and reflecting on the experience, I'm somewhat amazed at the amount of nice ideas that were presented in such a compact text. The book cannot be compared with more rigorous and comprehensive texts such as Rudin, but you still get all the fundamentals of Hilbert space plus some wonderful applications.
I must strongly disagree with the reader from Sao Paolo who says that chapters 12 and 13 are poorly motivated. These chapters are crucial for the final theorem of the book in chapter 16. Parrott's Theorem in chapter 12 is the key to the foundational Nehari's theorem of chapter 15. Chapter 13 explores Hardy spaces which are the setting place for the major theorem of Adamyan, Arov, and Krein in chapter 16. In fact, I found the movement of ideas from chapter 12 to chapter 16 to be marvelously compelling. These chapters have extreme importance for theoretically oriented control engineers.
Only a modicum of real and complex analysis is necessary to understand the book. Knowledge of measure theory is not required.
12 of 12 people found the following review helpful
Very Clear,short and useful
20 Oct 2000
Format:Paperback
The first eleven chapters are an excellent introduction to functional analysis . Both Hilbert and Banach spaces are introduced carefully. Then there are two short chapters on orthogonal expansions and classical fourier series and then linear operators are studied. From the point of view of a person who is interested in applications to physics and engineering one can say that the book is well motivated mainly because is so compact and because of the many notes on applications. Chapters nine , ten and eleven on Green's functions and eigenfunctions expansions are extremely good. Chapters twelve and thirteen are poorly motivated from the point of view of applications.Finally chapters fourteen to sixteen try to exhibit the applications to complex analysis of operator theory and be helpfull to eletrical engineers.I think the book fails in this. So the ten first chapters of the book are excellent . The remaining less so
11 of 11 people found the following review helpful
An unusually readable book on Hilbert space
12 Jun 2000
Format:Paperback
An unusually readable book on Hilbert space. Very clean notation and very detailed proofs. There are also numerous diagrams. There are also answers to selected problems, but no detailed solutions. If you own one book on Hilbert space, or even functional analysis, this should be it. The author takes great pains to illustrate the ideas involved, not just pound out the theorems.
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