A distributional Hardy transformation
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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1979-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000521 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850160736351813632 |
|---|---|
| author | R. S. Pathak J. N. Pandey |
| author_facet | R. S. Pathak J. N. Pandey |
| author_sort | R. S. Pathak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a4c9f9cfae8041fbad9286fce9cb70a5 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a4c9f9cfae8041fbad9286fce9cb70a52025-08-20T02:23:04ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012469370110.1155/S0161171279000521A distributional Hardy transformationR. S. Pathak0J. N. Pandey1Department of Mathematics, Banaras Hindu University, Varanasi, IndiaDepartment of Mathematics, Carleton University, Ottawa, CanadaThe 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.http://dx.doi.org/10.1155/S0161171279000521integral transformHardy transformHankel transformdistributionsgeneralized functions. |
| spellingShingle | R. S. Pathak J. N. Pandey A distributional Hardy transformation International Journal of Mathematics and Mathematical Sciences integral transform Hardy transform Hankel transform distributions generalized functions. |
| title | A distributional Hardy transformation |
| title_full | A distributional Hardy transformation |
| title_fullStr | A distributional Hardy transformation |
| title_full_unstemmed | A distributional Hardy transformation |
| title_short | A distributional Hardy transformation |
| title_sort | distributional hardy transformation |
| topic | integral transform Hardy transform Hankel transform distributions generalized functions. |
| url | http://dx.doi.org/10.1155/S0161171279000521 |
| work_keys_str_mv | AT rspathak adistributionalhardytransformation AT jnpandey adistributionalhardytransformation AT rspathak distributionalhardytransformation AT jnpandey distributionalhardytransformation |