Doctor of Philosophy (PhD)
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.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Yang, Yunyun, "A New Method In Distribution Theory With A Non-Smooth Framework" (2015). LSU Doctoral Dissertations. 1751.