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...
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| Datum: | 1996 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5263 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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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