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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 153, Pages 29–54 (Mi into362)  

On Gelfond–Leontiev Operators of Generalized Differentiation

A. V. Bratishchev

Don State Technical University, Rostov-on-Don

Abstract: The notion of the Gelfond–Leontiev operator of generalized differentiation in the space $H(G)$ of analytic functions in a simply connected domain $G$ is extended. Problems on the representation of such operators, the solvability of linear operator equations, the convergence of series of generalized exponentials, etc. are examined.

Keywords: operator of generalized differentiation, series of generalized exponentials, integral representation, multiplier, diagonal operator

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Bibliographic databases:
UDC: 517.53; 517.983
MSC: 30B40; 46E10; 47B47

Citation: A. V. Bratishchev, “On Gelfond–Leontiev Operators of Generalized Differentiation”, Complex analysis, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 153, VINITI, Moscow, 2018, 29–54

Citation in format AMSBIB
\Bibitem{Bra18}
\by A.~V.~Bratishchev
\paper On Gelfond--Leontiev Operators of Generalized Differentiation
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 153
\pages 29--54
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into362}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3903390}


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