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arXiv · 2202.09997

Differentiation operator in the Beurling space of ultradifferentiable functions of normal type on an interval

Natalia Abuzyarova
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Abstract

In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation invariant subspaces containing no exponential monomials. As an application, we describe the sets of solutions of finite and infinite systems of < > homogeneous convolution equations.

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Natalia Abuzyarova. 2022-02-21. Differentiation operator in the Beurling space of ultradifferentiable functions of normal type on an interval. https://arxiv.org/abs/2202.09997

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