On invariant subspaces of the Pommiez operator in the spaces of entire functions of exponential type. (English. Russian original) Zbl 07123860
J. Math. Sci., New York 241, No. 6, 760-769 (2019); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 142, 111-120 (2017).
Summary: We describe closed invariant eigenspaces of the Pommmiez operator in the (LF)-space of entire functions of exponential type. This space is topologically equivalent (by means of the Laplace transform) to the strong dual space of all germs of functions that are analytic on a convex, locally closed subset of the complex plane.
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 47B38 | Linear operators on function spaces (general) |
| 46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
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