Complex inversion and uniqueness theorems for a generalized Laplace transform

Gupta, Anubha; Mahato, Anil Kumar

doi:10.1016/0019-3577(91)90018-3

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1994

2020

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Cited by 3 publications

(2 citation statements)

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“…for every continuity point θ of F . There are many other related transforms for which an inversion formula is available (see [3,11,13]). However, as far as rates of convergence in these inversion theorems are concerned, it seems that little research has been done.…”

Section: φ(T)mentioning

confidence: 99%

Rates of uniform convergence in the real inversion theorem for Laplace transforms

Adell

Sangüesa

1999

Math. Proc. Camb. Phil. Soc.

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Section: φ(T)mentioning

confidence: 99%

Rates of uniform convergence in the real inversion theorem for Laplace transforms

Adell

Sangüesa

1999

Math. Proc. Camb. Phil. Soc.

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“…Recently Gupta and Mahato [2] extended the transform (1.2) to a class of generalized functions and an analyticity theorem is proved for it. In Gupta and Mahato [3], a complex inversion formula for (1.2) has been extended to a class of generalized functions.…”

Section: Introductionmentioning

confidence: 99%

Some Theorems on a Generalized Laplace Transform of Generalized Functions

Gupta¹,

Mahato²

1994

Tamkang J. Math.

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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.

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