Laplace Transform in Commutative Banach Algebras

Author: Dean, Robert Yost

Year: 1952

Degree: Dissertation (Ph.D.)

Advisor: Bohnenblust, Henri Frederic

Committee Member: Unknown, Unknown

Option: Mathematics; Physics

DOI: 10.7907/R8JF-GT33

Abstract

After a brief review of the general theory of commutative complex Banach algebras in Section I, Section II introduces and discusses some important facts about the generalized Laplace-Stieltjes integral. Section III consists of an investigation of the regions of ordinary and absolute convergence of the Laplace-Stieltjes integral, and is followed by specializations to Dirichlet and power series in Section IV. Section V contains a consideration of the analyticity of functions defined by Laplace-Stieltjes integrals, while Section VI concludes the thesis with some remarks on the existence and distribution of singularities of such functions.

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