Abstract
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.
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Zvozdetskii, T.I., Linchuk, S.S. Generalization of Berg-Dimovski convolution in spaces of analytic functions. Ukr Math J 48, 1028–1038 (1996). https://doi.org/10.1007/BF02390960
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DOI: https://doi.org/10.1007/BF02390960