Advertisement

The Generalized H- and G-transforms

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

Abstract

We already considered Mellin convolution type transforms with the H- and G-functions as kernels in the Chapter 3. As we have seen, the inversion formulae depend on the values of the k, μ (a) k = 0, μ > 1; b) k > 0 in Theorem 3.3 and c*, γ* (a) c* = 0, 1/2 < γ* ≤ 0, pq; b) c* = 0, γ* > 0; c) c* > 0 in Theorem 3.4) which are determined by the parameters of the H- and G-functions. This fact does not cause any troubles if we consider the particular cases of the H- and G-transforms. However, if we will investigate the H- and G- transforms as united objects, we will need new approach, which unites the studied cases with the new ones (k = 0, μ ≤ 1; k < 0; c* = 0, γ* ≤ - 1/2; c* < 0). This approach is based on the Parseval formula (3.45) and was studied by Vu Kim Tuan et al. (1986), Vu Kim Tuan (1987), S.G. Samko et al. (1987), Nguyen Thanh Hai and S.B. Yakubovich (1992).

Keywords

Integral Equation Important Method Similar Fact Inversion Formula Integral Transform 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations