Laplace Transform in Commutative Banach Algebras

Citation

Dean, Robert Yost (1952) Laplace Transform in Commutative Banach Algebras. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/R8JF-GT33. https://resolver.caltech.edu/CaltechTHESIS:11202017-144107731

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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