Some vector-valued laplace transforms (original) (raw)

Some Remarks on the Properties of Double Laplace Transforms

International Journal of Applied Physics and Mathematics, 2013

In this note, we have discussed and proved the different properties of double Laplace transforms like linearity property, change of scale, shifting property, double Laplace transform of partial derivatives, double Laplace transform of integral, multiplication by xt and division by xt.

Vector-valued laplace transforms and cauchy problems

Israel Journal of Mathematics, 1987

Linear differential equations in Banach spaces are systematically treated with the help of Laplace transforms. The central tool is an "integrated version" of Widder's theorem (characterizing Laplace transforms of bounded functions). It holds in any Banach space (whereas the vector-valued version of Widder's theorem itself holds if and only if the Banach space has the Radon-Nikod~m property). The Hille-Yosida theorem and other generation theorems are immediate consequences. The method presented here can be applied to operators whose domains are not dense.

A generalized Laplace transform of generalized functions

Analysis Mathematica, 1992

В работе дается распр остранение на случай обобщенных функций обобщенного преоб-р азования Лапласа Оно называется преоб разованием Вебера. Вв одится понятие трансформир уемоети по Веберу обобщенных функций. Д оказывается формула полного обращения и соответс твующая теорема единственности. Полу чено структурное опи сание одного класса обобще нных функций, трансформируемых по Веберу.

On the Discrete Laplace Transform

2019

The objective of this paper is to introduce the discrete Laplace transform. Basic theorems related to this transformation are mentioned and the discrete Laplace transform of basic functions are given.

Multiplicative Laplace transform and its applications

Optik - International Journal for Light and Electron Optics, 2016

In this work, taking definitions and properties of Laplace transform in classical analysis as a basis, we give some basic definitions and properties of the multiplicative Laplace transform. In addition, solutions of some multiplicative differential equations are obtained by the help of this transform.