The purpose of the paper is to give the state of the art on Michael's problem, the long-standing open question odf continuity of characters on commutative Fréchet algebras. We first quote two well-known consequences of the "abstract Mittag-Leffler theorem", the theorem of Arens, which shows that characters on finitely rationally generated Fréchet a...
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...
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...
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...
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 ...
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...
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...
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...
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} \...
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...
