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Comment: Published 1999, softcover, 128 pages. Some pages have underlining/writing marks in pencil.
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Elements of the Theory of Functions and Functional Analysis (Dover Books on Mathematics) Paperback – February 16, 1999


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Elements of the Theory of Functions and Functional Analysis (Dover Books on Mathematics) + Introductory Real Analysis (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 128 pages
  • Publisher: Dover Publications (February 16, 1999)
  • Language: English
  • ISBN-10: 0486406830
  • ISBN-13: 978-0486406831
  • Product Dimensions: 8.5 x 5.4 x 0.5 inches
  • Shipping Weight: 9.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #29,354 in Books (See Top 100 in Books)

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Customer Reviews

4.8 out of 5 stars
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This book is better than his fabulous Real Analysis book.
K. Selva
This book is appreciated not only because the topics it includes but mostly because of the insight with which it was written.
Bernardo Vargas
After looking through some other text books, I have to say that this is probably the best book I read.
Rakesh

Most Helpful Customer Reviews

69 of 71 people found the following review helpful By Paulo (paulovol@convex.com.br) on November 18, 1999
Format: Paperback
This book is divided into two parts. The first part is devoted mainly to metric and normed spaces. There are too a chapter on the essentials of set theory, an addendum on generalized functions, and a chapter on linear operators. The second part is devoted to measure theory, the Lebesgue integral, the theory of square integrable functions(L2) and Hilbert spaces. The second part incorporates exercises to the reader. The clarity of exposition and the elegancy of this book is notorious ! This book can be recommended not only for mathematicians, but for theoretical physicists. Do you know why the Heisenberg picture of quantum mechanics is equivalent to the Schrodinger picture of quantum mechanics ? Mathematically, Heisenberg theory uses the space l2, while Schrodinger theory uses the space L2. A consequence of the Riesz-Fisher theorem is that the spaces l2 and L2 are isomorphic, a result proved in this book. The two theories leads to the same physical results, and in consequence are equivalent, although different in the mathematical content ! You need to buy this book !
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56 of 57 people found the following review helpful By UNPINGCO on June 11, 2000
Format: Paperback
This book is actually two books bound as one. The first part concerns metric spaces and normed linear spaces. The second covers Lebesgue integration. The typesetting and prose are sometimes very tight, but some of the constructions used in the proofs are really amazing. Numerous examples are sprinkled through the text. I would not recommend this book as a first book in functional analysis or in Lebesgue integration. To get the most out of this book, you need to have seen many of the results presented elsewhere to really appreciate the Master's technique used in developing those same results in this book.
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75 of 82 people found the following review helpful By Bernardo Vargas on July 28, 2000
Format: Paperback
This highly regarded book came out from the notes of Andrei Kolmogorov's lectures given at Moscow's Lomonosov University in the 1940's, and it still stands as one of the best introductions to real analysis available.
The authors introduce step by step all the key concepts needed to get a thorough understanding of the subject and proceed all the way long from set theory to Fredholm integral equations.
This book is appreciated not only because the topics it includes but mostly because of the insight with which it was written. It is a pleasure to find through every page of the book the great genious of Kolmogorov who not only mastered most areas of mathematics but who also had an almost unparalleled understanding of what the trends of future mathematics would be.
The contents are: Elements of Set Theory; Metric and Topological Spaces; Normed and Topological Linear Spaces; Linear Functionals and Linear Operators; Elements of Differential Calculus in Linear Spaces; Measure, Measurable Functions, Integral; Indefinite Lebesgue Integral, Differentiation Theory; Spaces of Summable Functions; Trigonometric Series, Fourier Transformation; Linear Integral Equations.
Full motivation and detailed explanation for each topic. Short bibliography, but that is justified by the fact that the authors themselves were involved in the development of the topics covered.
Conclusion: a must-have text for every mathematician or math student.
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36 of 37 people found the following review helpful By Pedro L. Ribeiro on March 29, 2000
Format: Paperback
I must say that Kolmogorov is one of my favorite Russian scientists and scientific writers (the others are Arnol'd, Gel'fand and Landau). His approach over real and functional analysis is superb. But I have a serious complaint: why did Dover choose the old and dated Graylock edition to reprint this masterpiece? The most recent Russian edition has a lot of other important topics (missing in Dover's reprint), such as differential calculus in Banach spaces, which is so difficult to find a decent treatment of. The organization of the book is also better in the Russian edition. A good revised and translated reprint of it would deserve not five, but six, seven, ten stars...
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14 of 14 people found the following review helpful By K. Selva on March 7, 2007
Format: Paperback
This book is better than his fabulous Real Analysis book. It is one of the best, if not THE best, functional analysis book out there and the price is low. Quality to price ratio is approaching infinity here (as Dover reduces the price more)!!!

Kolmogorov knows how to arrange topics and introduce them at the proper spots throughout the book. Everything is broken down into bite sized pieces and you are given enough examples to digest what's going on. Reading the book is like reading Kolmogorov's mind, as he has tried to teach HOW TO THINK about the material, not just DO IT. It's also very addictive, even though it's rigorous.

Name a better functional analysis book? Not sure if that's possible.
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13 of 13 people found the following review helpful By Humberto Silva Rafe on October 10, 2004
Format: Paperback
I own the book in Spanish language. Some content in the book is not easy stuff, if you study by others books, but Kolmogorov has the gift to make easy things that aren't quite so easy. Perhaps some theory is "old", because all the new books use some diferent approach to the subject, like the chapter dedicated to the Lebesgue integral, the book give the definition of a simple function in a different manner that we use today. The book is a must to have in your library, when you need to work with Functional Analysis.
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19 of 22 people found the following review helpful By A Customer on May 18, 2001
Format: Paperback
This book is not quite up-to-date, but still very good as a starting point in (functional) analysis. The virtue of Kolmogorov and Fomin is their user-friendly writing style. I am delighted to find their book being available for less than ten dollars.
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