A distributional Hardy transformation
| Autor: | R. S. Pathak, J. N. Pandey |
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| Jazyk: | angličtina |
| Rok vydání: | 1979 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2, Iss 4, Pp 693-701 (1979) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 01611712 |
| DOI: | 10.1155/S0161171279000521 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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