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  • 标题:The Meijer transformation of generalized functions
  • 本地全文:下载
  • 作者:E. L. Koh ; E. Y. Deeba ; M. A. Ali
  • 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:1987
  • 卷号:10
  • 期号:2
  • 页码:267-286
  • DOI:10.1155/S0161171287000334
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    This paper extends the Meijer transformation, M μ , given by ( M μ f ) ( p ) = 2 p Γ ( 1 + μ ) ∫ 0 ∞ f ( t ) ( p t ) μ / 2 K μ ( 2 p t ) d t , where f belongs to an appropriate function space, μ  ϵ  ( − 1 , ∞ ) and K μ is the modified Bessel function of third kind of order μ , to certain generalized functions. A testing space is constructed so as to contain the Kernel, ( p t ) μ / 2 K μ ( 2 p t ) , of the transformation. Some properties of the kernel, function space and its dual are derived. The generalized Meijer transform, M ¯ μ f , is now defined on the dual space. This transform is shown to be analytic and an inversion theorem, in the distributional sense, is established.

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