In the class of linear continuous operators that act in the spaces of functions analytic in domains, we describe, in various forms, isomorphisms that commute with a power of the Gel’fond–Leont’ev generalized integration operator. We also obtain representations of all closed subspaces of the space of analytic functions that are invariant with respect to a power of the Gel’fond–Leont’ev generalized integration operator.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 61–68, January, 2011.
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Linchuk, N.E., Linchuk, S.S. On some properties of Gel’fond–Leont’ev generalized integration operators. Ukr Math J 63, 74–83 (2011). https://doi.org/10.1007/s11253-011-0488-x
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DOI: https://doi.org/10.1007/s11253-011-0488-x