Abstract:
We consider those elements of the Schwartz algebra of entire functions which are the Fourier-Laplace transforms of invertible distributions with compact supports on the real line. These functions are called invertible in the sense of Ehrenpreis. The first of the presented results is about the properties of zero subsets of invertible in the sense of Ehrenpreis function f. Namely, we establish some properties of the zero subset formed by zeros of f laying not far from the real axis. We also obtain estimates from below for |f| which generalize the corresponding ones in the definition of the notion of sine-type functions.
Keywords and phrases:
Schwartz algebra, entire function, distribution of zero sets, slowly decreasing function.
Citation:
N. F. Abuzyarova, “On properties of functions invertible in the sense of Ehrenpreis in the Schwartz algebra”, Eurasian Math. J., 13:1 (2022), 9–18
\Bibitem{Abu22}
\by N.~F.~Abuzyarova
\paper On properties of functions invertible in the sense of Ehrenpreis in the Schwartz algebra
\jour Eurasian Math. J.
\yr 2022
\vol 13
\issue 1
\pages 9--18
\mathnet{http://mi.mathnet.ru/emj428}
\crossref{https://doi.org/10.32523/2077-9879-2022-13-1-09-18}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4407201}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129908968}
Linking options:
https://www.mathnet.ru/eng/emj428
https://www.mathnet.ru/eng/emj/v13/i1/p9
This publication is cited in the following 4 articles:
N. F. Abuzyarova, Z. Yu. Fazullin, “Invariant subspaces in non-quasianalytic spaces of Ω-ultradifferentiable functions on an interval”, Eurasian Math. J., 15:3 (2024), 9–24
N. F. Abuzyarova, “Perturbations of an Integer Sequence as Zero Sets of Divisors
in Some Spaces of Entire Functions”, Math. Notes, 113:5 (2023), 613–623
N. F. Abuzyarova, Z. Yu. Fazullin, “On Properties of Zero Sets of Divisors in Weighted Spaces of Entire Functions”, Lobachevskii J Math, 44:6 (2023), 2192
A. M. Gaisin, B. E. Kanguzhin, A. A. Seitova, “Completeness of the exponential system on a segment of the real axis”, Eurasian Math. J., 13:2 (2022), 37–42
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