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Product Description
Please note the ISBN 9780486406831 includes 2 volumes in a single book. The pages are numbered separately for both volumes within the book.
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Customer Reviews
Most Helpful Customer Reviews
3 of 3 people found the following review helpful
Format:Paperback
Very good book for the beginner in functional theory. It also includes a very good introduction in topology. This book is well suited for science and engineering students or in general the novice in topology and function theory.
2 of 2 people found the following review helpful
Format:Paperback
This is another wonderful Dover classic; so a reprint of a first edition that later became a classic. Price, not much more than a cup of coffee. It stays fresh a lot longer though.
It is a serious mathematics book, and it has remained current now for two generations. The level is upper level undergraduate and beginning graduate.
But it is also a great book for someone who is looking for a quick overview of basic tools in function theory, and functional analysis.
Grant you that a lot has changed since the first printing in the 1940's.
Key topics in the book are as relevant now as then, e.g., (sample from the contents) Normed and Topological Linear Spaces; and their duals; Linear Operators; Differential Calculus and integrals; Measurable Functions, Integration theory; Summable functions; spectral theory; Trigonometric series, Fourier transformation; Fredholm Integral Equations.
Andrei Kolmogorov was a true pioneer in what is now modern mathematics, and its neighboring areas: probability theory, stochastic processes, harmonic analysis, information theory, dynamical systems.
One point where the coverage is limited is in its focus on linear theory. With hindsight we now know that non-linear features must be used in models for turbulence and other areas of applications.
The book is great, nonetheless, for selfstudy, or for a supplement to anyone of a number of courses in mathematics. Review by Palle Jorgensen, December 2011.
It is a serious mathematics book, and it has remained current now for two generations. The level is upper level undergraduate and beginning graduate.
But it is also a great book for someone who is looking for a quick overview of basic tools in function theory, and functional analysis.
Grant you that a lot has changed since the first printing in the 1940's.
Key topics in the book are as relevant now as then, e.g., (sample from the contents) Normed and Topological Linear Spaces; and their duals; Linear Operators; Differential Calculus and integrals; Measurable Functions, Integration theory; Summable functions; spectral theory; Trigonometric series, Fourier transformation; Fredholm Integral Equations.
Andrei Kolmogorov was a true pioneer in what is now modern mathematics, and its neighboring areas: probability theory, stochastic processes, harmonic analysis, information theory, dynamical systems.
One point where the coverage is limited is in its focus on linear theory. With hindsight we now know that non-linear features must be used in models for turbulence and other areas of applications.
The book is great, nonetheless, for selfstudy, or for a supplement to anyone of a number of courses in mathematics. Review by Palle Jorgensen, December 2011.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
16 reviews
55 of 57 people found the following review helpful
A MAGNIFIC BOOK !
18 Nov 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 !
46 of 47 people found the following review helpful
At the elbow of the Master...
12 Jun 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.
69 of 75 people found the following review helpful
Still one of the finest.
28 July 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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