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Elementary Functional Analysis (Dover Books on Mathematics) Paperback – January 18, 1996

ISBN-13: 978-0486689234 ISBN-10: 0486689239 Edition: 2nd

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 352 pages
  • Publisher: Dover Publications; 2nd edition (January 18, 1996)
  • Language: English
  • ISBN-10: 0486689239
  • ISBN-13: 978-0486689234
  • Product Dimensions: 8.4 x 5.4 x 0.7 inches
  • Shipping Weight: 13.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #1,184,730 in Books (See Top 100 in Books)

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: Russian

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Most Helpful Customer Reviews

62 of 62 people found the following review helpful By Jonathon Hay on August 14, 2000
Format: Paperback
This is volume 2 of Shilov's Moscow University course on Mathematical Analysis. If you have read Shilov's first volume ("Elementary Real and Complex Analysis") or his volume on Linear Algebra, then you can expect more of the same clear explanation and thoughtful organization of materials. His proofs are designed to help the reader understand material and provide deep insight into the mathematics involved. Highly recommended for those who want a consise -- but very thorough -- introduction to theory behind differential equations and Fourier analysis.
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36 of 39 people found the following review helpful By Palle E T Jorgensen VINE VOICE on August 26, 2007
Format: Paperback Verified Purchase
Elementary Functional Analysis by Georgi E. Shilov is suitable for a beginning course in functional analysis and some of its applications, e.g., to Fourier series, to harmonic analysis, to partial differential equations (PDEs), to Sobolev spaces, and it is a good supplement and complement to two other popular books in the subject, one by Rudin, and another by Edwards.
Rudin's book is entitled "Functional Analysis" (not in the Dover series) and it is my favorite. Rudin's book is of newer vintage, and it goes more in depth, and includes new material on unbounded operators in Hilbert space. Edwards' book "Functional Analysis: Theory and Applications;" is in the Dover series, and it is twice as thick as Shilov's book.
Topics covered in Shilov: Function spaces, L^p-spaces, Hilbert spaces, and linear operators; the standard Banach, and Hahn-Banach theorems. It includes many exercises and examples. Well motivated with applications.
Book Comparison:
Shilov book is gentler on students, and it is probably easier to get started with: It stresses motivation a bit more, the exercises are easier, and finally Shilov includes a few applications; fashionable these days. And of course, the books in the Dover series are cheap in comparison. Review by Palle Jorgensen, August 2007.
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13 of 16 people found the following review helpful By R. Cardoso on August 17, 2006
Format: Paperback
I enjoyed the last chapters of the book, that are relative to the applications: differential geometry, Fourier series, Fourier transform, differential equations.

Also I think that the study of the convergence of Fourier series partially based on the notion of delta-like sequences of functions is very interesting and possibly it enables some generalizations.

However the book is not self-contained because it does very much references to 'Linear Algebra' and 'Elementary Real and Complex Analysis' of the author.
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