Mathematics

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

Authors: Yurko V. A.

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

Authors: Nurmagomedov А. А.

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

Authors: Mazur T. V.

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

Authors: Burmistrova M. D.

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.

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

Authors: Alekseenkov V. V., Rasulov K. M.

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.