Abelian Theorem of Generalized Fourier-Stieltjes Transform

V. D. Sharma, P. D. Dolas

Abstract: The integral transform plays an important role in the solution of a wide class of problems of mathematical physics, for instance, boundary value problem for Laplace equation etc. Considerably which are used to solve the boundary value problems of Mathematical Physics and Partial Differential equation etc. In this paper, the generalization of Fourier- Stieltjes transform is presented. Abelian theorem of initial value type and final value type are proved. These results are widely used to solve the boundary value problems.

Keywords: Stieltjes transform, Fourier transform, Fourier-Stieltjes transform, generalized function, Testing function space