Open AccessSOME THEOREMS ON A GENERALIZED LAPLACE TRANSFORM OF GENERALIZED FUNCTIONS
Author(s) -
Awadhesh Chandra Gupta,
Anil Kumar Mahato
Publication year - 1994
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.25.1994.4459
Subject(s) - laplace transform , mathematics , beta (programming language) , convolution (computer science) , inversion (geology) , generalized function , inverse laplace transform , class (philosophy) , mellin transform , pure mathematics , mathematical analysis , combinatorics , paleontology , machine learning , artificial intelligence , computer science , artificial neural network , biology , programming language , structural basin
In this paper we extend the generalized Laplace transform \[F(s)=\frac{\Gamma(\beta+\eta+1)}{\Gamma(\alpha+\beta+\eta+1)}\int_0^\infty (st)^\beta\ _1F_1(\beta+\eta+1, \alpha+\beta+\eta+1; -st)f(t) dt\]where $f(t)\in L(0,\infty)$, $\beta\ge 0$, $\eta > 0$; to a class of generalized functions. We will extend the above transform to a class of generalized functions as a special case of the convolution transform and prove an inversion formula for it.