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Representation of Synthesizable Differentiation-Invariant Subspaces of the Schwartz Space
Doklady Mathematics ( IF 0.5 ) Pub Date : 2021-08-31 , DOI: 10.1134/s1064562421030029 N. F. Abuzyarova 1
中文翻译:
Schwartz 空间的可合成微分不变子空间的表示
更新日期:2021-09-01
Doklady Mathematics ( IF 0.5 ) Pub Date : 2021-08-31 , DOI: 10.1134/s1064562421030029 N. F. Abuzyarova 1
Affiliation
Abstract
We consider a differentiation-invariant subspace W in the Schwartz space \({{C}^{\infty }}(a;b)\) which admits weak spectral synthesis. We obtain the conditions under which W can be represented as the direct (algebraic and topological) sum of its residual subspace and the closed subspace spanned by the set of exponential monomials contained in W.
中文翻译:
Schwartz 空间的可合成微分不变子空间的表示
摘要
我们考虑Schwartz 空间\({{C}^{\infty }}(a;b)\)中的微分不变子空间W,它允许弱谱合成。我们获得了W可以表示为其残差子空间和由W 中包含的指数单项式集合跨越的闭子空间的直接(代数和拓扑)和的条件。