Introduction to Functional Analysis
Introduction to Functional Analysis This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and…
Specifikacia Introduction to Functional Analysis
Introduction to Functional Analysis
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 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. 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.
Familiarity with the basic theory of vector spaces and point-set topology is assumed, but 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.
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