The Extended Laplace Transform

Sabra, Ramadan

doi:10.3844/jmssp.2007.168.171

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“…For example the differential operator There arise the following question: Is it possible to know the important property as correctness of the equation Ax y = knowing properties of the sequence of operators that converges to the operator A? Also during present research (Radyno et al, 1993a;1993b;Tkan and Ramadan, 1992;Ramadan and Tkan, 1992;Ramadan and Jehad, 2000;Ramadan, 1993;1997;1998;1999;2007a;2007b;2007c) in many places were arisen questions about relationship between a special sequences of operators and their limits. In (Ramadan and Jehad, 2000) we proved the following theorems:…”

Section: Introductionmentioning

confidence: 63%

Sequences of Closed Operators and Correctness

Ramadan¹

2010

American Journal of Applied Sciences

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Section: Introductionmentioning

confidence: 63%

Sequences of Closed Operators and Correctness

Ramadan¹

2010

American Journal of Applied Sciences

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Ultra Linear Continuous Functionals and Ultra Generalized Complex Numbers in the Ultra Generalized Function Spaces

Sabra

2012

IJOPCSM

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New Algebra of New Generalized Functions

Sabra

2015

GSTF J Math Stat Oper Res

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In this paper, we define the vector space A(E) in which the associative multiplication is defined . Moreover we will define the embeddings of E , and E* into the algebra A(E) , where E be a locally convex algebra , and E* the dual space of E , that is E ⊂ E* ⊂ A(E) . The importance of the algebra A(E) that we can lift operations ( linear ond bilinear ) from the space E , and E* to the algebra A(E) , moreover we can define the multiplication of elements of E* as elements of the algebra A(E) . Also we introduce and study the case when E =S(R) the space of functions of rapid decay .

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The Extended Laplace Transform

Abstract: Abstract:The space of new generalized functions has been constructed. The operation of associative multiplication has been defined on this space. The Extended Laplace Transform has been defined.

Cited by 4 publications

References 4 publications

Sequences of Closed Operators and Correctness

Sequences of Closed Operators and Correctness

Ultra Linear Continuous Functionals and Ultra Generalized Complex Numbers in the Ultra Generalized Function Spaces

New Algebra of New Generalized Functions

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