A generalization of Laplace and Fourier transforms

2017/01/22 by Nikolaos Halidias, Halidias, Nikolaos
Engineering · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Elasticity and Wave Propagation #FOS: Mathematics #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.1701.06561

openalex publication_date 2017/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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