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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