Principal submodules in the module of entire functions, which is dual to the Schwarz space, and weak spectral synthesis in the Schwartz space

DOI10.1007/s10958-019-04453-0zbMath1426.30016OpenAlexW2967182010MaRDI QIDQ2331416

Yanyan Li

Publication date: 29 October 2019

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-019-04453-0

zbMATH Keywords

Fourier-Laplace transformspaces of entire functions\(D\)-invariant 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)

Related Items (max. 100)

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 ⋮ Principal submodules in the Schwartz module ⋮ Synthesizable sequence and principle submodules in Schwartz module ⋮ On zero setsof weakly localisable pricipal submodules in the Schwartz algebra ⋮ Differentiation operator in the Beurling space of ultradifferentiable functions of normal type on an interval

Cites Work

• Spectral synthesis in the Schwartz space of infinitely differentiable functions
• 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
• On the closure of characters and the zeros of entire functions
• Solution of Some Problems of Division. Part IV. Invertible and Elliptic Operators
• Solution of the Ehrenpreis factorization problem
• Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis
• Approximation of subharmonic functions
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