Topics in Hilbert Spaces, Spectral Theory, and Harmonic Analysis

General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory with a digression on Riesz bases. The second and third sections are focused on deriving the spectral theorem for Hilber...

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Bibliographic Details
Published inarXiv.org
Main Author Sawyer, Jack Robertson
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.09.2019
Subjects
Banach spaces
Codes
Fourier analysis
Group theory
Harmonic analysis
Hilbert space
Spectra
Spectral theory
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Summary:General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory with a digression on Riesz bases. The second and third sections are focused on deriving the spectral theorem for Hilbert spaces in finite and arbitrary dimension, respectively. The fourth and fifth sections present applications of the general theory: first to finite abelian groups, then to the space \(L^2(S^1,\mu)\).
ISSN:2331-8422