Mathematical Analysis - Vol 2: Elementary Functional Analysis

by Georgi E. Shilov

Book Overview

In this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0262191229
• ISBN13: 9780262191227
• Release Date: January 1974
• Publisher: MIT Press (MA)
• Length: 334 Pages
• Weight: 1.55 lbs.

Customer Reviews

A beginning course in functional analysis

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.

Excellent book

This book is well organized, concise, and easy to read. Overall a very good deal.

The book is very good but it is not self contained

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.

another great book from Shilov

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.