Geodesic
On properties of functions invertible in the sense of Ehrenpreis in the Schwartz algebra
Eurasian mathematical journal, Tome 13 (2022) no. 1, pp. 9-18 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{EMJ_2022_13_1_a1,
     author = {N. F. Abuzyarova},
     title = {On properties of functions invertible in the sense of {Ehrenpreis} in the {Schwartz} algebra},
     journal = {Eurasian mathematical journal},
     pages = {9--18},
     year = {2022},
     volume = {13},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a1/}
}
TY  - JOUR
AU  - N. F. Abuzyarova
TI  - On properties of functions invertible in the sense of Ehrenpreis in the Schwartz algebra
JO  - Eurasian mathematical journal
PY  - 2022
SP  - 9
EP  - 18
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a1/
LA  - en
ID  - EMJ_2022_13_1_a1
ER  - 
%0 Journal Article
%A N. F. Abuzyarova
%T On properties of functions invertible in the sense of Ehrenpreis in the Schwartz algebra
%J Eurasian mathematical journal
%D 2022
%P 9-18
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a1/
%G en
%F EMJ_2022_13_1_a1
N. F. Abuzyarova. On properties of functions invertible in the sense of Ehrenpreis in the Schwartz algebra. Eurasian mathematical journal, Tome 13 (2022) no. 1, pp. 9-18. http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a1/

[1] D. A. Abanina, “Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval”, Sib. Math. J., 53:3 (2012), 377–392

[2] N. F. Abuzyarova, “On shifts of the sequence of integers generating functions that are invertible in the sense of Ehrenpreis”, J. Math. Sci., 251 (2020), 161–175

[3] N. F. Abuzyarova, “On conditions of invertibility in the sense of Ehrenpreis in the Schwartz algebra”, Lobachevskii J. of Math., 42:6 (2021), 1141–1153

[4] Itogi Nauki Tekh., Ser. Sovrem. Mat., Fundam. Napravleniya, 54, 1989, 5–111

[5] C. A. Berenstein, B. A. Taylor, “A new look at interpolation theory for entire functions of one variable”, Adv. in Math., 33 (1980), 109–143

[6] R. P. Boas, jr., Entire functions, Acad. Press. Publ. Inc, NY, 1954

[7] L. Ehrenpreis, “Solution of some problems of division, IV”, Amer. J. Math., 57:1 (1960), 522–588

[8] L. Hörmander, “The analysis of linear partial di erential operators I”, Distribution theory and Fourier analysis, Springer-Verlag, Berlin–Heidelberg–New York–Tokyo, 1983

[9] B. Ya. Levin, Distribution of zero of entire functions, AMS Publ., Providence, Rhode Island, 1972

[10] R. Meise, B. A. Taylor, “Whitney's extension theorem for ultradifferentiable functions of Beurling type”, Ark. Mat, 25 (1988), 265–287