# Mathematics

## On Inverse Nodal and Spectral Problems for Boundary Value Problems with Discontinuity Conditions Inside the Interval

The solution of inverse nodal and inverse spectral problems is presented for second-order differential operators on a finite interval with discontinuity conditions inside the interval. Connections between these two classes of inverse problems are established.

## About Approximation Multinominals, Orthogonal on Any Grids

In this work are investigated approximation properties of multinominals pˆn(x), orthogonal with weight ∆tj on the any grids consisting of final number of points of a piece [−1, 1]. Namely the approximation formula, in which is established at increase n together with N, approximation behaviour of these multinominals close to approximation behaviour of multinominals Lasiandra.

## O РАЗРЕШИМОСТИ ОБРАТНОЙ ЗАДАЧИ ШТУРМА – ЛИУВИЛЛЯ В СИММЕТРИЧНОМ СЛУЧАЕ

Necessary and sufficient conditions are provided for the solvability of the inverse problem of recovering Sturm – Liouville operator from its spectrum in the central symmetry case.

## On Laguerre Expansions Summability by the Linear Methods

This paper studies a problem of Laguerre expansions summability via methods defined by triangular matrices. The conditions on a matrix and an expandable function are obtained to guarantee the convergence of corresponding linear means at the Lebesgue point t = 0.

## On the Equiconvergence of Expansions for the Certain Class of the Functional-Differential Operators with Involution on the Graph

The equiconvergence of expansions in eigen- and adjoint functions and trigonometric Fourier series is established for a 1-st order functional-differential operator on the graph-cycle.

## Three-Element Boundary Value Problem of Riemann Type for Metaanalytical Functions in a Circle

The article is devoted to the investigation of three-element boundary value problem of Riemann type for metaanalytical functions. A constructive method for solution of the problem in a circle was found. It is established that solution of the problem generally consists of solutions of two generalized and two usual scalar boundary value problems of Riemann for analytical functions in a circle.

## Approximating Properties of the Powers of the Differentiation Operator Resolvent

The families of operators are constructed and their approximating properties are investigated in the problems of approximating the derivative of function sand the smooth solutions of integralequations.

## The Mixed Problem for the Differential Equation with Involution and Potential of the Special Kind

For the solution of some mixed problem with involution and real symmetrical potential, explicit analytical formula has been found with the use of the Fourier method. Techniques allowing to avoid term-byterm differentiation of the functional series and impose the minimum conditions for initial problem data, are used.

## On a Approximate Solution of the Problem of Aspherical Convex Compact Set

We examine a finite-dimensional problem of minimizing the ratio radius of the ball given a compact convex set (in an arbitrary norm) to the radius of the inscribed sphere through the choice of a common center of these balls. The article offers an approach to building the numerical method of its solution.

## The Inverse Problem of Spectral Analysis for the Matrix Sturm – Liouville Equation

The inverse spectral problem is investigated for the matrix Sturm - Liouville equation on a finite interval. The article provides properties of spectral characteristics, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability has been obtained.