This article is cited in 2 papers

About the equality of the transform of Laplace to the transform of Fourier

A. V. Pavlov

Moscow Institute of Radio-technics, Electronics and Automatics (MTU), 78, Vernadsky Avenue, 119454 Moscow, Russia

Abstract: We proved that the transform of Laplace does not have complex part on the complex axis for the wide class of functions in different situations. The main theorem is proved presenting a function as sum of two Laplace transforms. The transforms are defined in the left and right parts of the plain accordingly. Such presentation is proved to be unique. With help of the results we obtain equality of the transforms of Laplace and Fourier for some class of functions.

Keywords: Laplace transform; Fourier transforms; Dirichlet problem; new inverse of Laplace transform.

UDC: 517.442, 517.443, 517.547.3

MSC: 44A10, 44A38

Received: 06.02.2016
Revised: 05.07.2016
Accepted: 30.06.2016

Language: English

DOI: 10.15393/j3.art.2016.3110

Bibliographic databases:

• 
•