International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1979 / Article

Open Access

Volume 2 |Article ID 713614 | https://doi.org/10.1155/S0161171279000521

R. S. Pathak, J. N. Pandey, "A distributional Hardy transformation", International Journal of Mathematics and Mathematical Sciences, vol. 2, Article ID 713614, 9 pages, 1979. https://doi.org/10.1155/S0161171279000521

A distributional Hardy transformation

Received23 Jan 1979

Abstract

The Hardy's F-transform F(t)=0Fv(ty)yf(y)dy is extended to distributions. The corresponding inversion formula f(x)=0Cv(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.

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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