O. A. Ivanova, S. N. Melikhov, “Cyclic vectors and invariant subspaces of the backward shift operator in Schwartz modules”, Funktsional. Anal. i Prilozhen., 2022, Volume 56, Issue 3,Pages <nobr>39

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Cyclic vectors and invariant subspaces of the backward shift operator in Schwartz modules

O. A. Ivanova^a, S. N. Melikhov^ab

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

Abstract: 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.

Keywords: backward shift operator, cyclic vector, invariant subspace, Schwartz module, Duhamel product.

UDC: 517.982+517.983.22

MSC: 30D15, 47B38, 46E10

Received: 01.02.2022
Revised: 05.04.2022
Accepted: 07.04.2022

DOI: 10.4213/faa3982