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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 153, Pages 55–68 (Mi into363)  

Pommier Operator in Spaces of Analytic Functions of Several Complex Variables

P. A. Ivanova, S. N. Melikhovab

a Southern Federal University, Rostov-on-Don
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: Pommier operators in spaces of analytic functions of several complex variables are examined. Linear continuous operators that commute with the system of Pommier operators in the space $A(\Omega)$ of analytic functions in a polycylindrical domain $\Omega$ and in the countable inductive limit of Fréchet weighted spaces of entire functions are described. Cyclic vectors of the system of Pommier operators in the space $A(\Omega)$ are studied.

Keywords: Pommier operator, commutant, cyclic vector, analytic function

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Bibliographic databases:
UDC: 517.9
MSC: 47B38, 47A16, 46E10

Citation: P. A. Ivanov, S. N. Melikhov, “Pommier Operator in Spaces of Analytic Functions of Several Complex Variables”, Complex analysis, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 153, VINITI, Moscow, 2018, 55–68

Citation in format AMSBIB
\Bibitem{IvaMel18}
\by P.~A.~Ivanov, S.~N.~Melikhov
\paper Pommier Operator in Spaces of Analytic Functions of Several Complex Variables
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 153
\pages 55--68
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into363}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3903391}


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