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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
  • 期号:4
  • 页码:693-701
  • DOI:10.1155/S0161171279000521
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    The Hardy's F -transform F ( t ) = ∫ 0 ∞ F v ( t y ) y f ( y ) d y is extended to distributions. The corresponding inversion formula f ( x ) = ∫ 0 ∞ C v ( t x ) t F ( t ) d t 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.

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