Generalization of Berg-Dimovski convolution in spaces of analytic functions
In the space H(G) of functions analytic in a ρ-convex region G equipped with the topology of compact convergence, we construct a convolution for the operator J π+L where J ρ is the generalized Gel’fond-Leont’ev integration operator and L is a linear continuous functional on H(G). This convolution is a generalization of the well-known Berg-Dimovski convolution. We describe the commutant of the operator J π+L in ℋ(G) and obtain the representation of the coefficient multipliers of expansions of analytic functions in the system of Mittag-Leffler functions.
English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 7, pp 1028-1038.
Citation Example: Zvozdetskii T. I. Generalization of Berg-Dimovski convolution in spaces of analytic functions // Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 910-919.