Editorial backlog

  1. Rakhimova A.I. Hypercyclic and chaotic operators in the space of analytic functions in the band
    Status: reviewing
    Abstract.     This article discusses the space $H(\Omega_r)$ of analytic functions in the band $\Omega_r$, endowed with the standard topology of uniform convergence on compacts of $\Omega_r$. It examines the issues of hypercyclicity, chaoticity and frequently hypercyclicity of differentiation and shift operators by definitions and using classical theorems. The main results of the article are given in Theorems 5, 10 and 11. In Theorem 5 it is proved that the linear continuous operator $T$ in $H(\Omega_r)$ commuting with the differential operator is hypercyclic. Theorem 10 shows that it is chaotic, and Theorem 11 is frequently hypercyclic in $H(\Omega_r)$.
    Date of submission: 10 Avgust 2023 г.


  2. Оценки жесткости кручения выпуклой области через новые геометрические характеристики области
    Status: reviewing
    Abstract.     В статье введены новые геометрические характеристики выпуклой области с конечной длиной границы и приведен алгоритм их вычисления. Доказан ряд изопериметрических неравенств между новыми функционалами и известными интегральными характеристиками области. Отметим, что некоторые неравенства имеют широкий класс экстремальных областей. Рассмотрены приложения новых характеристик к задаче об оценке жесткости кручения выпуклой области.
    Date of submission: 15 Avgust 2023 г.


  3. Krause Mean Processes Generated by Cubic Stochastic Matrices with Positive Influences
    Status: reviewing
    Abstract.     The Krause mean process serves as a comprehensive model for the dynamics of opinion exchange within multi-agent system wherein opinions are represented as vectors. In this paper, we propose a framework for opinion ex- change dynamics by means of the Krause mean process that is generated by a cubic doubly stochastic matrix with positive influences. The primary objective is to establish a consensus within the multi-agent system.
    Date of submission: 20 October 2023 г.


  4. Haliullin S.G. Extreme points for a total convex structure of generalized states
    Status: reviewing
    Abstract.     It is well known that the set of states of a certain quantum mechanical system is closed from the point of view of the operational approach if we want to form mixtures or convex combinations. That is, if $s_1$ and $s_2$ are states, then so are $\lambda s_1+(1-\lambda) s_2$, where $0 < \lambda < 1$, must be states. We can define a convex combination of elements in a linear space, but unfortunately, in the general case, linear space is artificial for a set of states and has no physical meaning, but the operation of forming mixtures of states has a natural meaning. For this reason, an abstract definition of mixtures will be given, which does not depend on the concept of linearity. We will call this space a convex structure. The paper will consider state spaces, spaces of generalized states in which pure states, operations, effects associated with operations are distinguished. We will also consider ultraproducts of sequences of these structures, operations and effects.
    Date of submission: 01 November 2023 г.


  5. Shishkin K.A., Gumerov R.N., Lipacheva E.V. A categorical criterion for the existence of universal $C^*$-algebras
    Status: reviewing
    Abstract.     The article deals with categories which determine universal $C^*$-algebras. These categories are called the compact $C^*$-relations. They were introduced by T.A.~Loring. For a given set $X$, the compact $C^*$-relation on $X$ is the category whose objects are functions from $X$ to $C^*$-algebras and morphisms are $\ast$-homomorphisms of $C^*$-algebras making the appropriate triangle diagrams commute. Moreover, these functions and $\ast$-homo\-mor\-phisms satisfy certain axioms. In this article, we prove that every compact $C^*$-relation is both complete and cocomplete. As an appli\-cation of the completeness of compact $C^*$-relations, we obtain the criterion for the existence of universal $C^*$-algebras.
    Date of submission: 03 November 2023 г.


  6. Podkletnova S.V. A series of boundary value problems for the Euler-Darboux equation with two lines of degeneracy
    Status: reviewing
    Abstract.     This paper introduces a new partial differential equation which is an extension of the well-known Euler-Poisson-Darboux equation. Based on the proven properties of the solution of the introduced equation, general solutions are found explicitly for various values of parameters, existence and uniqueness theorems are proved. Based on the general solutions of the introduced equation, Cauchy problems and modified Cauchy problems are set and solved in the area of the upper right-angled triangle. Explicit solutions are derived. The existence and uniqueness theorems of the solution of all the tasks are proved.
    Date of submission: 23 December 2023 г.


  7. On the Level Sets of the Generalized Resolvent Norm of Operators Pencils
    Status: reviewing
    Abstract.     This paper presents a proof demonstrating that the generalized resolvent operator, defined within a Hilbert space, cannot remain constant within any open subset of the resolvent set. We also study the same result over a complex uniformly convex Banach space under certain conditions. These findings extend existing results in the literature.
    Date of submission: 23 December 2023 г.


  8. Napalkov V.V., Nuyatov A.A. On the question of embedding Hilbert spaces with reproducing kernel
    Status: reviewing
    Abstract.     In this paper, necessary and sufficient conditions for embedding one Hilbert space with a reproducing kernel (RKHS) into another RKHS are obtained.This article is a continuation of the authors' works, in which the problem of the coincidence or equivalence of two RKHS's was studied. An important role is played by the condition of matching two two complete systems of functions with some linear continuous operator, introduced by the authors earlier. The results obtained are illustrated with specific examples.
    Date of submission: 27 December 2023 г.


  9. Nazarov S.A. Different types of localization for eigenfunctions of scalar mixed boundary value problems in thin polyhedra
    Status: reviewing
    Abstract.     Построена асимптотика собственных пар смешанной краевой задачи для оператора Лапласа в тонком многограннике с параллельными сближенными основаниями и скошенными узкими боковыми гранями. На основаниях назначены условия Дирихле, а на боковых гранях --- условия Дирихле или Неймана, распределение которых по граням, а также углы наклона последних оказывают существенное влияние на поведение собственных функций при истончении области. Обнаружены ситуации, в которых собственные функции распределены вдоль всего многогранника и локализованы около его боковых граней или вершин. Результаты основаны на анализе спектра (точка отсечки, изолированные собственные числа, пороговые резонансы и пр.) вспомогательных задач в полуполосе и четверти слоя со скошенными торцом и боковыми сторонами соответственно. Сформулированы открытые вопросы, относящиеся как к спектральному, так и асимптотическому анализу.
    Date of submission: 05 January 2024 г.


  10. Krivosheev A.S., Krivosheeva O.A. Interpolation and fundamental principle
    Status: reviewing
    Abstract.     In this paper we study the spaces of analytic functions in convex domains of the complex plane. We consider subspaces of such spaces. These subspaces are invariant with respect to the differentiation operator. The problem of the fundamental principle for the invariant subspace is investigated, i.e. the problem of representation all its elements using a series the eigenfunctions and associated functions of the differentiation operator in this subspace --- exponents and exponential monomials. We give a complete description of the space of sequences of the coefficients of series by which functions from the invariant subspace are represented. The problem of multiple interpolation in spaces of entire functions of exponential type is also studied. The duality of problems of interpolation and fundamental principle is considered. The problem of this duality is completely solved. The duality of the problems of fundamental principle and interpolation for an arbitrary convex domain without any restrictions is established.
    Date of submission: 07 January 2024 г.


  11. $(N,\varepsilon)$-PSEUDOSPECTRA OF CLOSED LINEAR OPERATORS ON ULTRAMETRIC BANACH SPACES
    Status: reviewing
    Abstract.     In this paper, we establish that the essential pseudospectrum of closed linear operator pencils is invariant under perturbation of completely continuous linear operators on ultrametric Banach spaces over a spherically complete field K and we obtain a characterization of the essential pseudospec- trum of a closed linear operator pencils by means of the spectra of any per- turbed completely continuous operators. Furthermore, we introduce and study the concept of (n,ε)-pseudospectrum of closed linear operators and the notion of (n,ε)-pseudospectrum of closed linear operator pencils on ultrametric Ba- nach spaces. We prove some results about them. Finally, several illustrative examples are provided.
    Date of submission: 02 February 2024 г.


  12. Kabanko M.V., Malyutin K.G. Interpolation sets in spaces of functions of finite order in the half-plane
    Status: reviewing
    Abstract.     Examples of interpolation sets in the space of functions of finite order that are analytic in the upper half-plane are given. These examples are similar to interpolation sets in the space of analytic bounded functions in the upper half-plane.
    Date of submission: 03 February 2024 г.


  13. Reconstruction of the Potential Function of Discontinuous Sturm-Liouville Operator from Spectral Data
    Status: reviewing
    Abstract.     This paper deals with the inverse spectral problem of the discontinuous Sturm-Liouville operator that is indicated in the way: to determine the potential $q(x)$ and the boundary constant $h$ according to spectral data. Finally, the reconstruction algorithm of the potential $q(x)$ from the spectral data is given.
    Date of submission: 07 February 2024 г.


  14. BOUND FOR CERTAIN HANKEL DETERMINANTS AND THE ZALCMAN CONJECTURE ASSOCIATED WITH MULTIVALENT BOUNDED TURNING FUNCTIONS OF ORDER ALPHA
    Status: reviewing
    Abstract.     In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound to the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions of order α, for α ∈ [0,1). Further, we estimate an upper bound for third and fourth Hankel determinants with respect to two-fold and three-fold symmetric functions belongs to the same class. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carathéodory class P.
    Date of submission: 09 February 2024 г.


  15. Kudasheva E.G., Menshikova E.B., Khabibullin B.N. Dual construction and the existence of (pluri)subharmonic minorant
    Status: reviewing
    Abstract.     Рассматривается проблемы существования и построения субгармонической или плюрисубгармонической функции, огибающей снизу функцию на подмножестве в конечномерном вещественном или комплексном пространстве. Такие проблемы естественным образом возникали в теориях равномерных алгебр, потенциала и комплексного потенциала, что нашло отражение в работах Д.~А.~ Эдвардса, Т.~В.~Гамелина, Е.~А.~Полецкого, С.~Бу и В.~Шахермайера, Б. Коула и Т.~Рансфорда, Ф. Ларуссона и Р. Сигурдссона и многих других. В наших работах 1990-х гг. и последних лет было показано, что эти проблемы играют ключевую роль при исследовании нетривиальности весовых пространств голоморфных функций, при описании нулевых множеств и подмножеств функций из таких пространств, в вопросах представления мероморфных функций в виде отношения голоморфных функций с ограничениями на их рост, при изучении аппроксимации экспоненциальными системами в функциональных пространствах и пр. Основные результаты статьи о существовании субгармонической или плюрисубгармонической функции-миноранты выводятся из нашей общей теоретико-функциональной схемы, которая позволяет дать двойственное определение нижней огибающей относительно выпуклого конуса в проективном пределе векторных решёток. Эта схема разрабатывалась нами в последние годы и основана на развитии абстрактной формы выметания. Идеология абстрактного выметания восходит к А. Пуанкаре и М.~В.~Келдышу в рамках выметания мер и субгармонических функций в теории потенциала. Она широко используется в теории вероятности, например, в известной монографии П.~Мейера, а также отражена, зачастую неявно, в монографиях Г.~П.~Акилова, С.~С.~Кутателадзе, А.~М.~Рубинова и др., связанных с теорией упорядоченных векторных пространств и решёток. В нашей статье разработанная нами схема адаптируется для выпуклых подконусов конуса всех субгармонических или плюрисубгармонических функций. Это позволяет получить новые критерии существования субгармонической или плюрисубгармонической миноранты для функций на области.
    Date of submission: 11 February 2024 г.


  16. Gladkov A.L. Global and blow-up solutions for a parabolic equation with nonlinear memory under nonlinear nonlocal boundary condition
    Status: reviewing
    Abstract.     In this paper we consider parabolic equation with nonlinear memory and absorption \begin{equation*} u_t= \Delta u + a \int_0^t u^q (x,\tau) \, d\tau - b u^m, \;x \in \Omega,\;t>0, \end{equation*} under nonlinear nonlocal boundary condition \begin{equation*} u(x,t) = \int_{\Omega}{k(x,y,t)u^l(y,t)}\,dy, \; x\in\partial\Omega, \; t > 0, \end{equation*} and nonnegative continuous initial datum. Here $ a, b,\,q, \,m,\,l $ are positive numbers, $\Omega$ is a bounded domain in $\mathbb{R}^N$ for $N\geq1$ with smooth boundary $\partial\Omega,$ $k(x,y,t)$ is a nonnegative continuous function defined for $x \in \partial \Omega$, $y \in \overline\Omega$ and $ t \ge 0.$ We prove that every solution of the problem is global if $\max (q,l) \leq 1$ or $\max (q,l) > 1$ and $ l < (m + 1)/2, \, q \leq m.$ For $l>\max\{1, (p+1)/2\}$ and positive for small values of $ t$ function $k(x,y,t)$ solutions blow up in finite time for large enough initial data. The obtained results improve previously established conditions for the existence and the absence of global solutions.
    Date of submission: 20 February 2024 г.


  17. Smirnov A.O., Шиловский S.D. О векторном производном нелинейном уравнении Шредингера
    Status: reviewing
    Abstract.     В работе предлагается последовательность пар Лакса, условиями совместности которых являются векторные интегрируемые нелинейные уравнения. Первыми уравнениями этой иерархии являются векторные уравнения Каупа-Ньюэлла, Чень-Ли-Лью и Герджикова-Иванова. Тип векторного уравнения зависит от дополнительного параметра $\alpha$. Предложенная нами форма векторного уравнения Каупа-Ньюэлла имеет небольшие отличия от классической. Показано, что эволюция простейших нетривиальных решений этих уравнений является композицией эволюции длины вектора решения и эволюции ориентации вектора решения. Исследованы свойства спектральных кривых простейших нетривильных решений векторных уравнений из построенной иерархии.
    Date of submission: 01 Mart 2024 г.


  18. Determining of a space dependent coefficient of fractional wave equation with the Generalized RiemannLiouville time derivative
    Status: reviewing
    Abstract.     This work investigates an initial-boundary value and an inverse coefficient prob- lem of determining a space dependent coefficient in the fractional wave equation with the generalized Riemann-Liouville (Hilfer) time derivative order 1 < α ≤ 2. In the beginning, it is considered the initial boundary value problem (direct problem). By the Fourier method, this problem is reduced to equivalent integral equations, which contain Mittag-Leffler type functions in free terms and ker- nels. Then, using the technique of estimating these functions and the generalized Gronwall inequality, we get apriori estimate for solution via unknown coefficient which will be used to study the inverse problem. The inverse problem is reduced to the equivalent integral equation of Volterra type. To show existence unique solution to this equation the Schauder principle is applied. The local existence and uniqueness results are obtained.
    Date of submission: 04 Mart 2024 г.


  19. The norming sets of $L_s(^6 \ell_1^2)$
    Status: reviewing
    Abstract.     ...
    Date of submission: 22 Mart 2024 г.