A generalization of Laplace and Fourier transforms
Classical Analysis and ODEs
2017-01-31 v2
Abstract
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization, some examples and basic properties. We also give the form of its inverse by using the theory of the Fourier transform. Finally, we apply the symmetric Laplace transform to a parabolic problem and to an ordinary differential equation.
Keywords
Cite
@article{arxiv.1701.06561,
title = {A generalization of Laplace and Fourier transforms},
author = {Nikolaos Halidias},
journal= {arXiv preprint arXiv:1701.06561},
year = {2017}
}