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Brief communications
Invariant subspaces in nonquasianalytic spaces of $\Omega$-ultradifferentiable functions on an interval
N. F. Abuzyarovaab a Institute of Mathematics with Computing Centre -- Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, 112 Chernyshevsky str., Ufa, 450008 Russia
b Ufa University of Science and Technology, 32 Zaki Validi str., Ufa, 450076 Russia
Abstract:
In this paper we consider a weakened version of the spectral synthesis for the differentiation operator in nonquasianalytic spaces of ultradifferentiable functions. We deal with the widest possible class of spaces of ultradifferentiable functions among all known ones. Namely, these are spaces of $\Omega$-ultradifferentiable functions which have been recently introduced and explored by A.V. Abanin. For differentiation invariant subspaces in these spaces, we establlish conditions of weak spectral synthesis. As an application, we prove that a kernel of a local convolution operator admits weak spectral synthesis. We also show that a conjunction of kernels of convolution operators admits weak spectral synthesis if all generating ultradistributions have the same support equaled to $\{0\}$ and there exists one generated by an ultradistribution which characteristic function is a multiplier in the corresponding space of entire functions.
Keywords:
ultradifferentiable functions, ultradistributions, Fourier-Laplace transform, invariant subspaces, spectral synthesis.
Received: 03.09.2022 Revised: 20.09.2023 Accepted: 26.09.2023
Citation:
N. F. Abuzyarova, “Invariant subspaces in nonquasianalytic spaces of $\Omega$-ultradifferentiable functions on an interval”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 11, 86–91
Linking options:
https://www.mathnet.ru/eng/ivm9919 https://www.mathnet.ru/eng/ivm/y2023/i11/p86
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