Spectral synthesis in the Schwartz space of infinitely differentiable functions

DOI10.1134/S1064562414050202zbMath1317.47007MaRDI QIDQ483675

Yong-Cai Geng, Sumit K. Garg

Publication date: 17 December 2014

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

spectruminvariant subspaceentire functionsspectral synthesisdifferentiation operatorweak localizability

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Invariant subspaces of linear operators (47A15) Topological linear spaces of continuous, differentiable or analytic functions (46E10)

Related Items (14)

On condition of representing a subspace in Schwartz space invariant with respect to differentiation as direct sum of its residual and exponential components ⋮ Preservation of classes of entire functions defined in terms of growth restrictions along the real axis under perturbations of their zero sets ⋮ Spectral synthesis for the differentiation operator in the Schwartz space ⋮ Functions in the Schwartz algebra that are invertible in the sense of Ehrenpreis ⋮ Principal submodules in the Schwartz module ⋮ Cyclic vectors and invariant subspaces of the backward shift operator in Schwartz modules ⋮ On shifts of the sequence of integers generating functions that are invertible in the sense of Ehrenpreis ⋮ On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis ⋮ Synthesizable sequence and principle submodules in Schwartz module ⋮ On zero setsof weakly localisable pricipal submodules in the Schwartz algebra ⋮ Representation of synthesizable differentiation-invariant subspaces of the Schwartz space ⋮ On conditions of invertibility in the sense of Ehrenpreis in the Schwartz algebra ⋮ Principal submodules in the module of entire functions, which is dual to the Schwarz space, and weak spectral synthesis in the Schwartz space ⋮ Differentiation operator in the Beurling space of ultradifferentiable functions of normal type on an interval

Cites Work

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• Subspaces of \(C^\infty\) invariant under the differentiation
• Derivation-invariant subspaces of \(C^{\infty}\)
• A new look at interpolation theory for entire functions of one variable
• Closed submodules of holomorphic functions with two generators
• On the closure of characters and the zeros of entire functions

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