Pommiez operator in spaces of analytic functions of several complex variables. (English. Russian original) Zbl 1458.32007
J. Math. Sci., New York 252, No. 3, 345-359 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 153, 55-68 (2018).
Summary: Pommiez operators in spaces of analytic functions of several complex variables are examined. Linear continuous operators that commute with the system of Pommiez 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 Pommiez operators in the space \(A(\Omega )\) are studied.
MSC:
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
| 47B38 | Linear operators on function spaces (general) |
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
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