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Mellin Convolution Type Transforms With Arbitrary Kernels

  • Semen B. Yakubovich
  • Yurii F. Luchko
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 287)

Abstract

In this section, following G.N. Watson (1933), E.C. Titchrnarsh (1937), Vu Kim Tuan (1986a), Vu Kim Tuan (1986b), Vu Kim Tuan (1987), Vu Kim Tuan et al. (1986), we consider the Mellin convolution type transforms of the form
$$ g\left( x \right) = \left[ {Kf} \right]\left( x \right) = \int_0^\infty {k\left( {xy} \right)} f\left( y \right)dy $$
(1)
such that their inverses have the similar form
$$ g\left( x \right) = \left[ {\hat Kf} \right]\left( x \right) = \int_0^\infty {\hat k\left( {xy} \right)} f\left( y \right)dy $$
(2)
where the kernel (x) is called the conjugate kernel.

Keywords

Inversion Formula Parseval Equality Watson Condition Dual Formula Mellin Convolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Semen B. Yakubovich
    • 1
  • Yurii F. Luchko
    • 1
  1. 1.Department of Mathematics and MechanicsBeylorussian State UniversityMinsk, ByelorussiaRussia

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