Cyclic vectors and invariant subspaces of the backward shift operator in Schwartz modules. (English. Russian original) Zbl 1522.47022
Funct. Anal. Appl. 56, No. 3, 188-198 (2022); translation from Funkts. Anal. Prilozh. 56, No. 3, 39-51 (2022).
Summary: Cyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of exponential type are described. The results are applied to describe ideals of the algebra of infinitely differentiable functions on a closed or open interval containing 0 with Duhamel product as multiplication.
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 47A15 | Invariant subspaces of linear operators |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 46E25 | Rings and algebras of continuous, differentiable or analytic functions |
Keywords:
backward shift operator; cyclic vector; invariant subspace; Schwartz module; Duhamel productReferences:
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