Title page for ETD etd-11052004-083332


Type of Document Dissertation
Author Mihai, Claudiu
Author's Email Address mihai2@math.lsu.edu
URN etd-11052004-083332
Title Asymptotic Laplace Transforms
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Frank Neubrander Committee Chair
Gestur Olafsson Committee Member
Jimmie Lawson Committee Member
Michael Tom Committee Member
William Adkins Committee Member
Donald Kraft Dean's Representative
Keywords
  • Laplace transforms
  • asymptotics
Date of Defense 2004-10-22
Availability unrestricted
Abstract
In this work we discuss certain aspects of the classical Laplace theory that are relevant for an entirely analytic approach to justify Heaviside's operational calculus methods. The approach explored here suggests an interpretation of the Heaviside operator ${cdot}$ based on the "Asymptotic Laplace Transform." The asymptotic approach presented here is based on recent work by G. Lumer and F. Neubrander on the subject. In particular, we investigate the two competing definitions of the asymptotic Laplace transform used in their works, and add a third one which we suggest is more natural and convenient than the earlier ones given. We compute the asymptotic Laplace transforms of the functions $tmapsto e^{t^n}$ for $nin N$ and we show that elements in the same asymptotic class have the same asymptotic expansion at $infty.$ In particular, we present a version of Watson's Lemma for the asymptotic Laplace transforms.

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