文章基本信息

标题：A distributional Hardy transformation
本地全文：下载
作者：R. S. Pathak ; J. N. Pandey
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1979
卷号：2
DOI：10.1155/S0161171279000521
出版社：Hindawi Publishing Corporation
摘要：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.