Esterle, Jean

A Picard-Borel algebra is a commutative unital complex algebra A such that every family of pairwise linearly independent invertible elements of A is linearly independent, and a Picard-Borel ideal I in a commutative complex unital algebra A is an ideal I of A such that the quotient algebra A/I is a Picard-Borel algebra. In a preliminary paper the au...

Gaisin, R. A.
Published in
Mathematical Notes

Abstract Problems of constructing regular majorants for sequences \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu=\{\mu_n\}_{n=0}^{\infty}$$\end{document} of number...

Zabolotskii, N. V. Mostova, M. R. Shvets, V. E.
Published in
Mathematical Notes

Abstract We study the relationship between the existence of an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upsilon$$\end{document}-density \documentclass[12pt]{min...

Abuzyarova, N. F.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper we study zero sets of entire functions in the Schwartz algebra. This algebra is defined as the Fourier–Laplace transform image of the space of all distributions compactly supported on the real line. We obtain the conditions under which given complex sequence forms zero set of some invertible in the sense of Ehrenpreis element ...

Khabibullin, B. N. Khabibullin, F. B.
Published in
Lobachevskii Journal of Mathematics

AbstractLet \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D$$\end{document} be a domain in the complex plane and \documentclass[12pt]{minimal} \usepackage{amsmath} \u...

Halder, Samar Sahoo, Pulak
Published in
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)

AbstractWe study uniqueness problems in terms of shared values or shared sets for a large class of entire functions representable as Dirichlet series in some right half-plane. In this article, we obtain a result that extends a recent result due to Oswald and Steuding [Ann. Univ. Sci. Budapest., Sect. Comput. 48 (2018), 117–128 (2018)]. Our result i...

Krivosheev, A. S. Krivosheeva, O. A.
Published in
Mathematical Notes

Abstract 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 obta...

Gabdrakhmanova, L. A. Khabibullin, B. N.
Published in
Russian Mathematics

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{C}$\end{document} be the complex plane, E be a measurable subset of a segment \documentclass[12pt]{minimal} \...

Yanchenko, A. Ya. Podkopaeva, V. A.
Published in
Mathematical Notes

The paper deals with the class of entire functions that increase not faster than exp{γ∣z∣6/5(ln∣z∣)−1} and that, together with their first derivatives, take values from a fixed field of algebraic numbers at the points of a two-dimensional lattice of general form (in this case, the values increase not too fast). It is shown that any such functions i...

Braichev, G. G.
Published in
Mathematical Notes

The paper deals with an entire function of noninteger order with a sequence of negative roots having (for this order) zero lower and finite upper densities. Sharp estimates for the lower indicator of such a function are obtained. It is proved that, in some angles, this characteristic is identically zero, and its form in the other angles is obtained...