Introductory Functional Analysis with Applications (Paperback)

by Erwin Kreyszig (Author) "Functional analysis is an abstract branch of mathematics that originated from classical analysis..." (more)
Key Phrases: total orthonormal set, total orthonormal sequence, uniform operator convergence, Spectral Properties of Self-Adjoint Operators, Properties of the Spectral Family, Hence Theorem (more...)

Editorial Reviews

Product Description
Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.

Product Details

• Paperback: 704 pages
• Publisher: Wiley; 1 edition (February 23, 1989)
• Language: English
• ISBN-10: 0471504599
• ISBN-13: 978-0471504597
• Product Dimensions: 8.9 x 5.9 x 1.3 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars See all reviews (14 customer reviews)
• Amazon.com Sales Rank: #123,432 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

36 of 37 people found the following review helpful:

5.0 out of 5 stars The Place to Start, July 22, 2003

By	Jason Schorn "j schorn" (Spokane, WA) - See all my reviews (REAL NAME)

Heir professor Kreyszig has done what the majority of other authors have failed to do. Namely, he has compiled a book whose only real prerequisites are a solid understanding of Calculus and some familiarity with Linear Algebra. Obviously this required level of understanding is minimal, to say the least, and this is one of the main reasons I feel so strongly that this book is number one in its category. Moreover, since the majority of "introductory" texts on Functional Analysis are primarily directed toward graduate students the aforementioned requirements coupled with a wide selection of topics makes this book easily accessible to advanced undergraduates and begining graduate students. I highly recommend this book to anyone interested in actually learning Functional Analysis and also to the ambitious self-learner since Kreyszig has included both hints and solutions to selected exercises. In regards to the exercises and examples contained in the text, they are well chosen, insightful and at no time does Kreyszig leave a major theorem/propostion to the reader. In fact, he provides many fully worked examples which are left as exercises in most other texts. My hat goes off to professor Kreyszig for such a wonderfully well written text and also to Wiley for continuing to publish this classic.

28 of 30 people found the following review helpful:

5.0 out of 5 stars Functional analysis - as it should be taught, April 25, 2002

By	Nathaniel Jewell (Adelaide, Australia) - See all my reviews

Most books on analysis could be subtitled "One damn theorem after another: written by mathematicians for mathematicians". This book is different. Though rigorous and concise, it takes the time to explain what theorems really mean and why concepts are worth understanding. It shows that functional analysis is a generalization and extension of many concepts from undergraduate algebra and calculus. As such, it is powerful, beautiful, and above all, useful.

The first half of the book covers the basic theory of metric spaces, normed/Banach spaces and inner-product/Hilbert spaces. Applications include approximation theory and numerical integration; differential and integral equations; and the Legendre, Hermite, Laguerre and Chebyshev polynomials. The second half of the book is devoted to spectral theory, the final chapter discussing operators in quantum mechanics. Although integration theory is not formally covered, the book does show its relationship to functional analysis.

The book provides numerous examples, counter-examples and exercises. The exercises really are do-able - mostly short but instructive - and answers are provided for odd-numbered questions.

18 of 19 people found the following review helpful:

5.0 out of 5 stars A fantastic introduction to functional analysis, August 27, 2000

By	KARTIK KRISHNAN S. (Hamilton, Ontario Canada) - See all my reviews

Kreyszig's "Introductory Functional Analysis with Applications", provides a GREAT introduction to topics in real and functional analysis. This book is part of the WILEY CLASSICS LIBRARY and is extremely well written, with plenty of examples to illustrate important concepts. It can provide you with a solid base in these subjects, before one takes on the likes of Rudin and Royden.

I had purchased a copy of this book, when I was taking a graduate course on real analysis and can only strongly recommend it to anyone else.