An Introduction to Functional Analysis (Hardcover) (ISBN-13: 9780521899642)

This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert-Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn-Banach theorem, the Krein-Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.

Author: James C. Robinson
ISBN-10: 0521899648
ISBN-13: 9780521899642
Publisher: Cambridge University Press
Language: English
Published: 03/12/2020
Pages: 416
Format: Hardcover
Weight: 1.50lbs
Size: 8.80h x 6.20w x 1.00d