Geodesic
Invariant subspaces in non-quasianalytic spaces of $\Omega$-ultradifferentiable functions on an interval
Eurasian mathematical journal, Tome 15 (2024) no. 3, pp. 9-24

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We consider and solve a weakened version of the classical spectral synthesis problem for di erentiation operator in non-quasianalytic spaces of ultradi erentiable functions (UDF). Moreover, we deal with the widest class of UDF among all known ones. Namely, we study the spaces of $\Omega$-ultradifferentiable functions introduced by Alexander Abanin in 2007–08. For subspaces of these spaces which are invariant under the di erentiation operator we establish general conditions of weak spectral synthesis. 
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     title = {Invariant subspaces in non-quasianalytic spaces of $\Omega$-ultradifferentiable functions on an interval},
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N. F. Abuzyarova; Z. Yu. Fazullin. Invariant subspaces in non-quasianalytic spaces of $\Omega$-ultradifferentiable functions on an interval. Eurasian mathematical journal, Tome 15 (2024) no. 3, pp. 9-24. http://geodesic.mathdoc.fr/item/EMJ_2024_15_3_a1/