Vol. 61, No. 2, 1975

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An inversion of the S2 transform for generalized functions

L. S. Dube

Vol. 61 (1975), No. 2, 383–390
Abstract

Define S2 transform of a member f of a certain space of generalized functions as

F(x) = ⟨f(t),K (t,x)⟩

where

        {
logxx−∕tt, x ⁄= t
K(t,x) =  1,     x = t
x

(0 < t < ,0 < x < ).

It is shown that

 lim Hn,x[F(x)] = f(x)
n→∞

in the weak distributional sence. Here Hn,x is a certain linear generalized differential operator.

Mathematical Subject Classification 2000
Primary: 46F10
Secondary: 44A05
Milestones
Received: 10 December 1974
Revised: 24 July 1975
Published: 1 December 1975
Authors
L. S. Dube