The Spectral Theorem for Self-Adjoint Operators

ECU Author/Contributor (non-ECU co-authors, if there are any, appear on document)

Kenneth Chilcoat (Creator)

Institution

East Carolina University (ECU )

Web Site: http://www.ecu.edu/lib/

Abstract: The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing a functional calculus that extends the intuitive notion of evaluating a polynomial on an operator. The Spectral Theorem is fundamentally important to operator theory and has applications in many fields, especially harmonic analysis on locally compact abelian groups. This thesis represents a merging of two traditional treatments of the Spectral Theorem and includes an extended example highlighting an important application in harmonic analysis.

Additional Information

Publication

Thesis

Language: English

Date: 2023

Subjects

Hilbert Space

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