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An Introduction to Functional Analysis

Authors

James C. Robinson
, University of Warwick
Published 2020

Description

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,…

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Key features

  • Includes an extensive source of homework problems for instructors and independent study
  • Presents functional analytical methods without a reliance on measure-theoretic results, making the topics more widely accessible
  • Provides readers with a sense of accomplishment and closure by showing how both Hilbert space theory and Banach space theory aim towards major results with important applications

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