**Analyticity theorem and operation-transform formula for LAPLACE - MELLIN INTEGRAL TRANSFORM TO A CLASS OF GENERALIZED FUNCTION**

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Dr.M.M.P.Singh and Mrs. Mampi Saha

Dr.M.M.P.Singh and Mrs. Mampi Saha

We have Extended Laplace-Mellin Integral Transformation (LMIT) to a class of Generalized Function. In this paper we discuss the ‘Testing Function Space’ ?LM?_(a,b,c,d ) and its dual ??LM?^'?_(a,b,c,d ). We have proved that ?LM?_(a,b,c,d ) is ‘Complete Space’. We have derived some lemmas those are ‘?? E?^(-SL) M^(P-1)?LM?_(a,b,c,d )’ , ‘D(I) is a subspace of ?LM?_(a,b,c,d )’ and ‘?LM?_(A,B,C,D ) is a dense subspace of E(I)’ . ‘Analyticity Theorem’ of Laplace-Mellin Integral Transformation has been derived and ‘Some Operation transformation formula’ for this transform has been proved.