1986•SIAM Journal on Mathematical AnalysisRequires access

The Representation of Functions as Laplace and Laplace–Stieltjes Transforms

F. J. Wilson

Abstract

We develop necessary and sufficient conditions for a function to be represented as a Laplace or Laplace–Stieltjes transform by considering the behaviour of the function on a single vertical line. Various kernels, based on ideal inversion kernels for the Fourier transform, are considered and three new inversion formulae for the Laplace transform are developed.

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Key concepts: Laplace–Stieltjes transform, Post's inversion formula, Laplace transform, Mathematics, Laplace transform applied to differential equations, Two-sided Laplace transform, Inverse Laplace transform, Mellin transform