Geodesic
Invariant subspaces with zero density spectrum
Ufa mathematical journal, Tome 9 (2017) no. 3, pp. 100-108 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper we show that each analytic solution of a homogeneous convolution equation with the characteristic function of minimal exponential type is represented by a series of exponential polynomials in its domain. This series converges absolutely and uniformly on compact subsets in this domain. It is known that if the characteristic function is of minimal exponential type, the density of its zero set is equal to zero. This is why in the work we consider the sequences of exponents having zero density. We provide a simple description of the space of the coefficients for the aforementioned series. Moreover, we provide a complete description of all possible system of functions constructed by rather small groups, for which the representation by the series of exponential polynomials holds.
Keywords: A series of exponential monomials, relatively small clusters, basis
Mots-clés : convex domain. 
@article{UFA_2017_9_3_a9,
     author = {O. A. Krivosheeva},
     title = {Invariant subspaces with zero density spectrum},
     journal = {Ufa mathematical journal},
     pages = {100--108},
     year = {2017},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_3_a9/}
}
TY  - JOUR
AU  - O. A. Krivosheeva
TI  - Invariant subspaces with zero density spectrum
JO  - Ufa mathematical journal
PY  - 2017
SP  - 100
EP  - 108
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UFA_2017_9_3_a9/
LA  - en
ID  - UFA_2017_9_3_a9
ER  - 
%0 Journal Article
%A O. A. Krivosheeva
%T Invariant subspaces with zero density spectrum
%J Ufa mathematical journal
%D 2017
%P 100-108
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/UFA_2017_9_3_a9/
%G en
%F UFA_2017_9_3_a9
O. A. Krivosheeva. Invariant subspaces with zero density spectrum. Ufa mathematical journal, Tome 9 (2017) no. 3, pp. 100-108. http://geodesic.mathdoc.fr/item/UFA_2017_9_3_a9/

[1] G. Polya, “Eine Verallgemeinerung des Fabryschen Luckensatzes”, Nachr. Geselesch Wissensch. Gottingen, 1927, 187–195 | Zbl

[2] G. Polya, “Untersuchungen uber Lucken und Singularitaten von Potenzreihen”, Math. Zeits., 29 (1928), 549–560 | DOI | MR

[3] B. Ya. Levin, Distribution of zeros of entire functions, Amer. Math. Soc., Providence, RI, 1980 | MR

[4] G. Valiron, “Sur les solutions des equations differentielles lineares d'ordre infinit et a coefficients constants”, Ann. Ec. Norm. Sup. Sér. 3, 1929:46, 25–53 | MR | Zbl

[5] I. F. Krasichkov-Ternovskii, “Comparison of entire functions of integral order by the distribution of their roots”, Matem. Sborn., 70(112):2 (1966), 198–230 (in Russian) | Zbl

[6] A. S. Krivosheyev, “Bases “in relatively small groups””, Ufimskij Matem. Zhurn., 2:2 (2010), 67–89 (in Russian) | Zbl

[7] A. S. Krivosheyev, “An almost exponential basis”, Ufimskij Matem. Zhurn., 2:1 (2010), 87–96 (in Russian)

[8] A. S. Krivosheyev, “An almost exponential sequence of exponential polynomials”, Ufa Math. J., 4:1 (2012), 82–100 | MR

[9] O. A. Krivosheyeva, “Convergence domain for series of exponential polynomials”, Ufa Math. J., 5:4 (2013), 82–87 | DOI | MR

[10] A. S. Krivosheev, O. A. Krivosheeva, “A basis in an invariant subspace of analytic functions”, Sb. Math., 204:12 (2013), 1745–1796 | DOI | DOI | MR | Zbl

[11] A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. Math., 68:2 (2004), 291–353 | DOI | DOI | MR | Zbl

[12] A. S. Krivosheev, O. A. Krivosheeva, “Fundamental principle and a basis in invariant subspaces”, Math. Notes, 99:5 (2016), 685–696 | DOI | DOI | MR | Zbl

[13] I. F. Krasichkov-Ternovskii, “Invariant subspaces of analytic functions. III. On the extension of spectral synthesis”, Math. USSR-Sb., 17:3 (1972), 327–348 | DOI | MR

[14] I. F. Krasichkov-Ternovskii, “Invariant subspaces of analytic functions. II. Spectral synthesis of convex domains”, Math. USSR-Sb., 17:1 (1972), 1–29 | DOI | MR

[15] O. A. Krivosheyeva, “Singular points of the sum of a series of exponential monomials on the boundary of the convergence domain”, St.-Petersburg Math. J., 23:2 (2012), 321–350 | DOI | MR | Zbl