Invariant Subspaces in Non-Quasianalytic Spaces of \( \Omega \)-Ultradifferentiable Functions on an Interval


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Authors

  • Natalia Abuzyarova
  • Ziganur Fazullin

Keywords:

\( \Omega \)-ultradifferentiable function, \( \Omega \)-ultradistribution, Fourier-Laplace transform, invariant subspace, spectral synthesis

Abstract

We consider and solve a weakened version of the classical spectral synthesis problem for differentiation operator in non-quasianalytic spaces of ultradifferentiable 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 differentiation operator we establish general conditions of weak spectral synthesis.

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Published

2024-11-17

How to Cite

Abuzyarova, N., & Fazullin, Z. (2024). Invariant Subspaces in Non-Quasianalytic Spaces of \( \Omega \)-Ultradifferentiable Functions on an Interval. Eurasian Mathematical Journal, 15(3), 09–24. Retrieved from https://emj.enu.kz/index.php/main/article/view/412

Issue

Vol. 15 No. 3 (2024)

Section

Articles