The Fields of the Convolution Quotients
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.
KeywordsFixed Function Convolution Operator Operational Calculus Generalize Hypergeometric Function Quotient Field
Unable to display preview. Download preview PDF.