On the Laplace transform of absolutely monotonic functions
Stamatis Koumandos, Henrik L. Pedersen
TL;DR
This paper establishes precise conditions under which a function can be represented as the Laplace transform of an absolutely monotonic function, providing a comprehensive characterization of such transforms.
Contribution
It offers necessary and sufficient criteria for a function to be the Laplace transform of an absolutely monotonic function, expanding theoretical understanding in this area.
Findings
Derived necessary and sufficient conditions for Laplace transforms of absolutely monotonic functions
Presented related results connecting monotonicity and Laplace transforms
Enhanced theoretical framework for analyzing Laplace transforms of monotonic functions
Abstract
We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.
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Taxonomy
TopicsMathematical Inequalities and Applications · Mathematical functions and polynomials · Functional Equations Stability Results