Portal de Periódicos da CAPES

An inversion formula for a distributional finite-Hankel-Laplace transformation

1979; Mathematical Sciences Publishers; Volume: 80; Issue: 2 Linguagem: Inglês

10.2140/pjm.1979.80.313

1945-5844

B. R. Bhonsle, R. A. Prabhu,

Matrix Theory and Algorithms

In this paper a Finite-Ήankel-Laplace transformation of a certain generalized functions is defined, and an inversion formula is established.1* Introduction.Schwartz first introduced the Fourier transform of distributions in 1947.Since then, extension of the classical integral transformation to generalized functions has been of continuing interest.Some pertinent references are [1], [2], [3], [4], [5], [7], [8], and [9].The classical Finite-Hankel-Laplace transform of function / defined on -oo<£<oo ?0<τ/<lis defined as (1.1)where J n (z) is the Bessel function of first kind of order n ^ -1/2 and j lf j 2 , is are positive zeros of J n (z) arranged in ascending order.An inversion theorem for the transform (1.1) is as follows.