Mathematics

One counterexample of shape-preserving approximation

Authors: Pleshakov M. G., Tyshkevich S. V.

Let 2s points yi=−π≤y2s<… Example. For each k∈N, k>2, and n∈N there a function f(x):=f(x;s,Y,n,k) exists, such that f∈Δ(1)(Y) and

About reversibility states of linear differential operators with periodic unbounded operator coefficients

Authors: Didenko V. B.

For investigated linear differential operator (equation) with unbounded periodic operator coefficients defined at one of the Banach space of vector functions defined on all real axis difference operator (equation) with constant operator coefficient defined at appropriate Banach space of two-side vector sequences is considered. For differential and difference operators propositions about kernel and co-image dimensions coincidence, simultaneous complementarity of kernels and images, simultaneous reversibility, spectrum interrelation are proved.

Weighted Integrability of Sums of Series with Respect to Multiplicative Systems

Authors: Fadeev R. N., Volosivets S. S.
A necessary and sufficient condition for Lp-integrability with power weight of a function f represented by the series with respect to multiplicative systems with generalized monotone coefficients is obtained. The integrability of the majorant of partial sums of a representing series is also described by the same conditions. In addition we study the integrability of difference quotient (f(x) − f(0))/x.

On Subvariety of Variety Generated by a Simple Infinite Lie Algebra of Cartan Type General Series W2

Authors: Bogdanchuk O. A.
We consider numerical characteristics of Lie algebras variety over a field of characteristic zero, basically, the exponent of variety.
Here, was constructed the infinite series of varieties of Lie algebras with different fractional exponents, which belong to variety
generated by a simple infinite Lie algebra of Cartan type general series W2.

Projective and injective descriptions in the complex domain. Duality

Authors: Shishkin A. B.

Research of a invariant subspaces of a differential operators infinite order in a complex domain generated many issues, related with transition to dual problems. This work devoted overcome these difficulties 

On an inverse problem for differential operators on hedgehog-type graphs

Authors: Yurko V. A.

An inverse spectral problem is studied for Sturm–Liouville differential operators on hedgehog-type graphs with generalized matching conditions in the interior vertices and with Dirichlet boundary conditions in the boundary vertices. A uniqueness theorem of recovering potentials from given spectral characteristics is provided, and a constructive solution for the inverse problem is obtained. 

About harmonic analysis of periodic at infinity functions

Authors: Strukova I. I.

We consider slowly varying and periodic at infinity multivariable functions in Banach space. We introduce the notion of Fourier series of periodic at infinity function, study the properties of Fourier series and their convergence. Basic results are derived with the use of isometric representations theory. 

Mixed problem for simplest hyperbolic first order equations with involution

Authors: Burlutskaya M. S., Khromov A. P.

In this paper investigates the mixed problem for the first order differential equation with involution at the potential and with periodic boundary conditions. Using the received refined asymptotic formulas for eigenvalues and eigenfunctions of the corresponding spectral problem, the application of the Fourier method is substantiated. We used techniques, which allow to avoid investigation of the uniform convergence of the series, obtained by term by term differentiation of formal solution on method of Fourier.

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