The \(h\)-Laplace and \(q\)-Laplace transforms
type: Item
instance of: scholarly article
title: The \(h\)-Laplace and \(q\)-Laplace transforms
zbMATH Open document ID: 1188.44008
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-02-19T00:00:00Z
review text: For a given function \(x\) with complex values the \(h\)-Laplace transform is defined as \[ (h/(1+hz))\sum^\infty_{k=0}x(kh)/(1+ hz)^k, \] and the \(q\)-Laplace transform as \[ (q-1)\sum^\infty_{n=0} q^nx(q^n)/\prod^n_{k=0} (1+(q- 1)q^k z), \] where \(z\) is the complex variable in the image domain. Most properties of the usual Laplace transform are transferred to these two transforms. It is shown that all these transforms are special cases of a more general Laplace transform on time scales.
Mathematics Subject Classification ID: 44A55
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 5673256
zbMATH Keywords: \(h\)-Laplace transform
zbMATH Keywords: \(q\)-Laplace transform
zbMATH Keywords: time scales
zbMATH Keywords: convolution
zbMATH Keywords: inverse transform
author: Martin Bohner
author: Gusein Sh. Guseinov
reviewed by: Lothar Berg
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.09.061
OpenAlex ID: W2061810827
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DOI: 10.1016/J.JMAA.2009.09.061
description: scientific article; zbMATH DE number 5673256