Geodesic
Invariant Spaces of Entire Functions
Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 380-396

Voir la notice de l'article provenant de la source Math-Net.Ru

Subspaces of the space of analytic functions on a convex domain in the complex plane that are invariant with respect to the differentiation operator are studied. The problem of continuing all functions in an invariant subspace to entire functions is investigated. A simple geometric criterion for the existence of such a continuation is obtained. A criterion for the functions from an invariant subspace to be represented by a series of exponential monomials is also obtained. These monomials are the eigenfunctions and generalized eigenfunctions of the differentiation operator on the invariant subspace.
Keywords: invariant subspace, analytic continuation, exponential monomial, entire function, series of exponentials. 
@article{MZM_2021_109_3_a5,
     author = {A. S. Krivosheev and O. A. Krivosheeva},
     title = {Invariant {Spaces} of {Entire} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {380--396},
     publisher = {mathdoc},
     volume = {109},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a5/}
}
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A. S. Krivosheev; O. A. Krivosheeva. Invariant Spaces of Entire Functions. Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 380-396. http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a5/