**Abanin A.V.**Sampling sets for the space of holomorphic functions of polynomial growth in a ball. Pp. 3 - 14**Abstract**: We develop a new approach to study sampling sets in the space of holomorphic functions of polynomial growth in a ball in the sense of Horowitz, Korenblum, and Pinchuk (Michigan Math. J., 44:2, 1997). It is based on involving weakly sufficient sets for intermediate inductive limits. By means of this approach we obtain a complete topological description of such sets and, as an application of this description, some new properties of sampling sets of general and special type are established. In particular, the main result of the above mentioned paper on sampling sequences of circles is extended to the multi-dimensional case.

**Aitkuzhina N.N., Gaisin A.M.**Exactness of estimates for \(k\)th order of Dirichlet series in a semi-strip. Pp. 15 - 23**Abstract**: We study the Dirichlet series converging only in a half-plane such that their sequence of exponents admits an extension to a “regular” sequence. We proved the exactness of two-sided estimates for \(k\)-order of the sum of the Dirichlet series in a semi-strip whose width depends on the special distribution density of the exponents.

**Bikmetov A.R., Vil'danova V.F., Khusnullini I.Kh.**On perturbation of a Schrödinger operator on axis by narrow potentials. Pp. 24 - 31**Abstract**: We consider a Schrödinger operator on the axis with two complex-valued potentials depending on two small parameters. One these parameters describes the length of the supports of the potentials, while the other corresponds to the maximal values of the absolute values of the potentials. We obtain the sufficient condition ensuring the emergence of an eigenvalues from the threshold of the essential spectrum. The asymptotics for this eigenvalue is constructed.

**Braichev G.G.**The exact bounds of lower type magnitude for entire function of order \(\rho\in(0,1)\) with zeros of prescribed average densities. Pp. 32 - 57**Abstract**: We provide exact two-sided estimates for lower type magnitude of entire functions of order \(\rho\in(0,1)\). The zeroes of these functions have prescribed upper and lower average densities and are arbitrarily distributed in the complex plane or on a ray. We analyze the obtained results and compare them them with known facts for entire functions of usual type.

**Girya N.P., Favorov S.Yu.**Various definitions of the spectrum of almost periodic functions. Pp. 58 - 70**Abstract**: We consider various definitions of spectrum for almost periodic functions in a finite dimensional space for uniform, Stepanov, Weil, Besicovitch metrics. We prove that in these cases the classical definition of spectrum is equivalent to an analogue of definition of Beurling spectrum.

**Ivanova О.А., Melikhov S.N.**On the orbits of analytic functions with respect to a Pommiez type operator. Pp. 71 - 75**Abstract**: Let \(\Omega\) be a simply connected domain in the complex plane containing the origin, \(A(\Omega)\) be the Fréchet space of all analytic on \(\Omega\) functions. An analytic on \(\Omega\) function \(g_0\) such that \(g_0(0)=1\) defines the Pommiez type operator which acts continuously and linearly in \(A(\Omega)\). In this article we describe cyclic elements of the Pommiez type operator in space \(A(\Omega)\). Similar results were obtained early for functions \(g_0\) having no zeroes in domain \(\Omega\).

**Kanguzhin B.E., Tokmagambetov N.E.**Convolution, Fourier transform and Sobolev spaces generated by non-local Ionkin problem. Pp. 76 - 87**Abstract**: In this work, given a second order differential operator \(\mathcal B\) subject to non-local boundary conditions, we assign Fourier transform and convolution to this problem. We study the properties of the introduced convolution and describe the class of test functions. We also introduce Sobolev spaces and obtain Plancherel identity related to operator \(\mathcal B\).

**Korobeinik Yu.F.**On some problems in the theory of the Riemann's zeta-function. Pp. 88 - 93**Abstract**: We determine the principal value of some integrals related to Riemann's zeta-function. We propose a probably new hypothesis which implies the famous Riemann's hypothesis on the absence of zeroes of zeta-function in the half-plane \(\Re z>1/2\), as well as some other facts in the theory of zeta-function.

**Kulaev R.Ch.**Comparison theorems for Green function of a fourth order boundary value problem on a graph. Pp. 94 - 103**Abstract**: In the work we develop the non-oscillation theory for fourth order equations on a geometric graph arising in modelling of rod junctions. The non-oscillation of an equation is defined in terms of the properties of a special fundamental system of solutions to the homogeneous equation. We describe the relation between non-oscillation property and the positivity of Green function to some classes of boundary value problems for fourth order equation on a graph.

**Murtazin Kh.Kh., Fazullin Z.Yu.**Formula of the regularized trace for perturbation in the Schatten–von Neumann of discrete operators. Pp. 104 - 110**Abstract**: In the paper we study a formula of the regularized trace for a perturbation in Schatten–von Neumann class (\(\sigma_p\), \(p\in\mathbb N\)) of discrete self-adjoint operators. We prove that the regularized vanishes after deducting \((p−1)\) terms of perturbation theory if there are no dilating gaps in the spectrum of the unperturbed operator.

**Trynin A.Yu.**On some properties of sinc approximations of continuous functions on the interval. Pp. 111 - 126**Abstract**: We study approximation properties of various operators being the modifications of sinc approximations of continuous functions on an interval.

**Shamoyan F.A.**On a class of inner functions in a half-space. Pp. 127 - 139**Abstract**: In the paper we obtain necessary and sufficient conditions for the weight vector function, under which a given inner function is weakly invertible in the weighted functions of holomorphic functions in a tubular domain.

**Sherstyukova O.V.**The problem on the minimal type of entire functions of order \(\rho\in(0,1)\) with positive zeroes of prescribed densities and step. Pp. 140 - 148**Abstract**: We consider the problem on the least possible type of entire functions of order \(\rho\in(0,1)\), whose zeroes lie on a ray and have prescribed densities and step. We prove the exactness of the estimate obtained previously by the author for the type of these functions. We provide a detailed justification for the construction of the extremal entire function in this problem.

**Kondratyuk A.A., Khoroshchak V.S.**Stationary harmonic functions on homogeneous spaces. Pp. 149 - 153**Abstract**: Stationary harmonic functions on homogeneous spaces are considered. A relation to double periodic harmonic functions of three variables is showed.

**Bërdëllima A.**About a conjecture regarding plurisubharmonic functions. Pp. 154 - 165**Abstract**: In this work we present Khabibullin's conjecture in its different equivalent forms. Applying the concept of the integral operator, we transform the original conjecture into a new form which proves to be helpful in studying it by means of the Laplace transform. Using Laplace transform of integral inequalities, we are able to show the uniqueness of a solution that satisfies both inequalities with identity. Furthermore we provide a new proof of Khabibullin's theorem by methods of the Laplace transform and contour integration from complex analysis. However, this method of transform fails to prove the conjecture and a brief reasoning is provided.

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