Identifier

etd-04132015-160154

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work, we present a complete treatment of the theory of thick distributions and its asymptotic expansion. We also present several applications of thick distributions in mathematical physics, function spaces, and measure theory. We also discuss regularization using different surfaces. In the last chapter we present some recent applications of distributions in clarifying the moment terms in the heat kernel expansion, and in explaining the relation between the heat kernel expansion and the cylinder kernel expansion.

Date

2015

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Estrada, Ricardo

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