The Spectral Theorem for Self-Adjoint Operators
Author
Chilcoat, Kenneth
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.
Subject
Date
2016-04-25
Citation:
APA:
Chilcoat, Kenneth.
(April 2016).
The Spectral Theorem for Self-Adjoint Operators
(Master's Thesis, East Carolina University). Retrieved from the Scholarship.
(http://hdl.handle.net/10342/5344.)
MLA:
Chilcoat, Kenneth.
The Spectral Theorem for Self-Adjoint Operators.
Master's Thesis. East Carolina University,
April 2016. The Scholarship.
http://hdl.handle.net/10342/5344.
December 04, 2023.
Chicago:
Chilcoat, Kenneth,
“The Spectral Theorem for Self-Adjoint Operators”
(Master's Thesis., East Carolina University,
April 2016).
AMA:
Chilcoat, Kenneth.
The Spectral Theorem for Self-Adjoint Operators
[Master's Thesis]. Greenville, NC: East Carolina University;
April 2016.
Collections
Publisher
East Carolina University