Synthesizable sequence and principle submodules in Schwartz module

DOI10.13108/2020-12-3-11zbMath1463.30124OpenAlexW3110281770MaRDI QIDQ5138429

Natal'Ya Fairbakhovna Abuzyarova

Publication date: 3 December 2020

Published in: Ufimskii Matematicheskii Zhurnal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/ufa521

zbMATH Keywords

Fourier-Laplace transformentire functionsspectral synthesisSchwarz spacelocal description of submodules

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Special classes of entire functions of one complex variable and growth estimates (30D15) Spaces and algebras of analytic functions of one complex variable (30H99)

Cites Work

• Unnamed Item
• Spectral synthesis in the Schwartz space of infinitely differentiable functions
• Subspaces of \(C^\infty\) invariant under the differentiation
• Derivation-invariant subspaces of \(C^{\infty}\)
• Spectral synthesis for the differentiation operator in the Schwartz space
• Synthesizable differentiation-invariant subspaces
• Principal submodules in the Schwartz module
• Principal submodules in the module of entire functions, which is dual to the Schwarz space, and weak spectral synthesis in the Schwartz space
• Complementability of exponential systems
• LOCAL DESCRIPTION OF CLOSED IDEALS AND SUBMODULES OF ANALYTIC FUNCTIONS OF ONE VARIABLE. II
• On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis
• Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis