Functional Analysis

Book Details

• Publisher: Dover Publications

• Author: Frigyes Riesz

• Language: English

• Edition: 1

• ISBN: 9780486464213

• Pages: 506

• Cover: Paperback

• Dimensions: 8.4 x 5.4 x 1.1 inches

About The Book

Functional Analysis by Frigyes Riesz is a celebrated text in the field of mathematics that offers a comprehensive treatment of modern theories of differentiation and integration. This classic work is renowned for its thorough exploration of the principal problems and methods used to handle integral equations, linear functionals, and transformations.

The book is divided into two main parts. Part one begins with a direct proof of the Lebesgue theorem on the differentiation of monotonic functions, followed by a detailed exploration of the Lebesgue integral. It covers important spaces such as L2 and Lp, and their associated linear functionals. The Stieltjes integral and its generalizations are also introduced, with a focus on their applications in linear operations on the space of continuous functions.

Part two delves into integral equations, including the Fredholm alternative and methods for solving completely continuous functional equations. It also explores the spectral theory of self-adjoint transformations in Hilbert spaces and the study of unbounded symmetric transformations. The book concludes with an examination of Von Neumann’s spectral theory and applications of methods from the theory of functions.

This text is a fundamental resource for advanced undergraduates, graduate students, and researchers in mathematics, particularly those interested in functional analysis, spectral theory, and the mathematical foundations of integration and differentiation. It provides a rigorous and detailed exposition of essential topics in these areas, making it a must-have for any serious student of the subject.