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Functional Analysis

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Author: Paul Garrett
Url: http://www.math.umn.edu/~garrett/m/fun/
Format: Ps, Pdf
Category: Functional Analysis
Pages: 200
Clicks: 4693

Description
Contents: Metric spaces; Spaces of functions; Hilbert spaces; Banach spaces; Applications of Banach space ideas to Fourier series; operators on Hilbert space; spectral theorem for self-adjoint compact operators on Hilbert spaces; topological vector spaces; categorical constructions; vector-valued integrals; Banach-Alaoglu, variant Banach-Steinhaus, bipolars, weak-to-strong principles; vector-valued holomorphic functions, weak-to-strong holomorphy; Measurable choice functions ; Schwartz-function envelopes of rapidly decreasing; Weak smoothness implies strong smoothness; Uniqueness of invariant distributions; Hahn-Banach theorems; Catalogue of topological vector spaces; Distribution-theoretic proof of Poisson Summation Formula; A good spectral theorem; Bernstein's analytic continuation of complex powers of polynomials.

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