International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 4, Pages 693-701
doi:10.1155/S0161171279000521
A distribution Hardy transformation
R.S. Pathak1
and J.N. Pandey2
1Department of Mathematics, Banaras Hindu University, Varanasi, India
2Department of Mathematics, Carleton University, Ottawa, Canada
Abstract
The Hardy's F-transform F(t)=∫0∞Fv(ty)yf(y)dy is extended to distributions. The corresponding inversion formula f(x)=∫0∞Cv(tx)tF(t)dt is shown to be valid in the weak distributional sense. This is accomplished by transferring the inversion formula onto the testing function space for the generalized functions under consideration and then showing that the limiting process in the resulting formula converges with respect to the topology of the testing function space.