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


Views: 5 / PDF downloads: 3

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.

Downloads

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

Section

Articles