Mathematics

Projection Description of Bessel Sequences

Authors: Terekhin P. A.

We consider Bessel sequences in Banach space with respect to modeling sequences space. The generalized analogues of theorems of Bari, Schur, Novikov and Czaja are established.

 

Same Properties r-fold Integration Series on Fourier – Haar System

Authors: Sharapudinov I. I., Muratova G. N.

Approximation properties of series obtained by r-fold integration of Fourier – Haar series are research. It is shown that r-fold integrated Fourier – Haar series can be useful in the task of simultaneous approximation of differentiable function and its derivatives.

Certain Caseofthe Riemann–Hilbert Boundary Value Problem with Peculiarities of Coefficients

Authors: Shabalin P. L.

We consider the Riemann – Hilbert boundary value problem for a case where the coefficients have countable set of discontinuity points of the first kind such that the series of jumps of argument of the coefficient function is divergent, but the index of the Hilbert problem is finite. We derive the formulae for general solution of the problem and investigate the picture of solvability.

On Propertiesofthe Eigenfunctionsofa Quadratic Pencilofthe Second Order Differential Operators

Authors: Rykhlov V. S.

The degenerated second order ordinary differential quadratic pencil with constant coefficients is considered. The case is studied, when the roots of characteristic equation lie on a straight line coming through the origin and on the both side of the origin. Properties of the system of its eigenfunctions in the spaces L2[0,σ], σ > 0 is investigated. Criteria of one-fold completeness and minimality of this systemareprovedandsufficientconditionsofone-foldcompleteness and minimality are found.

Factoring of an Entire Function into Two Equivalent Functions

Authors: Pismennyj R. G.

The article contains the development of the known KrasichkovTernovskii’s theorem about fission on event of the proximate order. Herewith event of the zero order is covered. Proof is realized on the same scheme and is founded on Adamara’s theorem.

Haar Series on Compact Zero-Dimensional Abelian Group

Authors: Lukomskii S. F.

In this article we construct a Haar system on compact zerodimensional abelian group as shifts and powers of some characters system. We find conditions under which a Fourier-Haar series of continuous function converge uniformly. We find groups for which Haar functions generated from one function by the operation of shifts, powers and dilations.

Extremal Rational Functions on Several Arcs of the Unit Circle with Zeros on these Arcs

Authors: Lukashov А. L., Tyshkevich S. V.

The solution of anextrema lproblem aboutrational function with fixed denominator and leading coefficient of nominator which is deviatedleast from zero on several arcs of the unit circle is given under restrictions on the location of zeros and additional conditions on mutual position of the arcs and zeros of denominator. The extremal function is represented in terms of the density of harmonic measure.

Solution of Integral Equations via Resolvents of Simplest Differential Operators

Authors: Khromov A. A.

Families of operators for approximate solution of integral equations with unbounded inverse operators and right parts of equations specified by the root-mean-square approximations are constructed.

On Uniform Convergenceof Transformationsof Fourier Serieson Multiplicative Systems

Authors: Agafonova N. Y.

Necessary and suffiecient conditions for uniform Λ-summability of Fourier – Vilenkin series of Functions from Orlicz spaces LΦ[0,1) and L1[0,1) are obtained. Some corollaries for matrices with generalized monotone coeffiecients are given.