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The Fields of the Convolution Quotients

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

Abstract

In previous Chapters 15, 18, we have constructed the convolution rings (Lα,*,+), (Cα, * λ ,+) with respect to the corresponding convolutions and without divisors of zero. For example, as we have seen in Theorem 18.8, multiple Erdelyi-Kober fractional integration operator (18.4) on the space Cα is reduced to multiplication by the fixed function h(x) (18.41) in the ring(Cα, * λ ,+). In this chapter we will obtain similar representation for the multiple Erdelyi-Kober fractional differentiation operator (18.16). This representation is valid in some field, which contains the ring(Cα, * λ ,+). We will also study convolution (15.1) for the Kontorovich-Lebedev transform (6.52) with the fixed function h(x) and extend the ring Lα to the field of convolution quotients. This chapter will be devoted to the description of this fields.

Keywords

Fixed Function Convolution Operator Operational Calculus Generalize Hypergeometric Function Quotient Field 
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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