An Introduction to Hilbert Space (Cambridge Mathematical Textbooks) [Paperback]

N. Young (Author)

Book Description

Publication Date: July 29, 1988 | ISBN-10: 0521337178 | ISBN-13: 978-0521337175

This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for 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. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book 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.

Editorial Reviews

Review

"...presents a very clear and elegant exposition of the basic notions of the theory of Hilbert space...It is beautiful and relatively recent mathematics..." Mathematical Reviews

Book Description

The notion of a Hilbert space is a central idea in functional analysis and this text demonstrates its applications in numerous branches of pure and applied mathematics.

Product Details

• Paperback: 254 pages
• Publisher: Cambridge University Press (July 29, 1988)
• Language: English
• ISBN-10: 0521337178
• ISBN-13: 978-0521337175
• Product Dimensions: 8.9 x 6 x 0.6 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #221,205 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

14 of 14 people found the following review helpful:

4.0 out of 5 stars A Tantalizing Introduction to Hilbert Space, February 26, 2002

By 

Neal Jameson "nealwj3" (Cambridge, MA United States) - See all my reviews
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This review is from: An Introduction to Hilbert Space (Cambridge Mathematical Textbooks) (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:

5.0 out of 5 stars Very Clear,short and useful, October 20, 2000

By 

Francisco Coutinho (Sao Paulo, Sao Paulo Brazil) - See all my reviews
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This review is from: An Introduction to Hilbert Space (Cambridge Mathematical Textbooks) (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:

5.0 out of 5 stars An unusually readable book on Hilbert space, June 12, 2000

By 

UNPINGCO (Los Angeles, CA) - See all my reviews

This review is from: An Introduction to Hilbert Space (Cambridge Mathematical Textbooks) (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.