Methods of Modern Mathematical Physics Vol.1: Functional Analysis – Michael Reed, Barry Simon – 1st Edition


This is the first of a multivolume series devoted to an exposition of functional analysis in modern mathematical . It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes.

We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, , and partial differential equations.

Table of Content

  • Preliminaries

  • Hilbert Spaces

  • Banach Spaces

  • Topological Spaces

  • Locally Convex Spaces

  • Bounded Operators

  • The Spectral Theorem

  • Unbounded Operators

  • The Fourier Transform

  • Supplementary Material

  • List of Symbols

  • Index

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