Volume 14, Issue 4

Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary
Abanin A. V., Varziev V. A.

We consider LB   spaces of functions which are holomorphic in a convex domain and have a finite type with respect to an order near its boundary. Using Laplace transformation, we give a description of their duals. Then we characterize mimimal absolutely representing systems of exponential functions in these spaces and prove that they always exist.

Inversion and description of the ranges of potentials with singularities of their kernels on a sphere
Gil A. V., Nogin V. A.

Within the framework of the method of approximative inverse operators we construct the inversion of generalized Strichartz potentials with densities in the Hardy space H 1   in the non-elliptic case, when their symbols degenerate on a set of measure zero. The ranges of these operators are also described.

Article (rus.) - [pdf] [zip-pdf]

Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case
Gusachenko V. V., Levenshtam V. B.

A concrete (illustrative) example of the linear parabolic problem with two independent variables and high-frequency coefficients in time is considered. The corresponding stationary homogeneous averaged problem is degenerate. Using the method developed recently for an ordinary differential equations [1] and the method of boundary layer a full formal asymptotics of the periodic solution in time is constructed.

Article (rus.) - [pdf] [zip-pdf]

The asimptotics of conditionally periodic solution of differential equation containing great high-frequency terms
Ishmeev M. R.

It was constructed and justified the full asimptotic of conditionally periodic solution for the systems of non-linear differential equations containing items proportional to some degrees of frequency.

Article (rus.) - [pdf] [zip-pdf]

About Green's function of a parabolic problem on a graph
Kulaev R. Ch.

The work is devoted to Green's function of the mixed boundary problem for equation of parabolic type on geometrical graph. Existence, continuity and positivity of Green's function are studied.

Article (rus.) - [pdf] [zip-pdf]

Banach lattices of continuous sections
Kusraev A. G., Tabuev S. N.

The aim of this note is to outline some application of ample continuous Banach bundles to the theory of Banach lattices.

Article (eng.) - [pdf] [zip-pdf]

On Maharam polynomials
Kusraeva Z. A., Tasoev B. B.

A Radon-Nikodym type theorem is proved and the Maharam extension is constructed for positive orthogonally additive polynomials in vector lattices.

Article (rus.) - [pdf] [zip-pdf]

On correlation of two solution classes for Navier-Stokes equations. II
Levenshtam V. B.

This is a supplement to the author's work [1] devoted to the solvability of initial boundary value problem for the Navier-Stokes equations with mass force y depeding on unknown (speed) polynomially. In this paper local resolvability of the problem in the generalized sense is established and the proof of a key lemma in [1] is also given.

Article (rus.) - [pdf] [zip-pdf]

On optimal recovery of the Laplacian of a function from its inaccurately given Fourier transform
Sivkova E. O.

The paper is devoted to the problem of the optimal recovery for a fractional power of the Laplacian of a function from its inaccurately given Fourier transform in metric L ∞   on some convex subset of ℝ d . The optimal recovery method is constructed. This method is not used the information about the Fourier transform outside some ball centred at the origin.

Article (rus.) - [pdf] [zip-pdf]

Using homological methods~on the base of iterated spectra in functional analysis
Smirnov E. I.

We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or H -limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular H -limit are projective and inductive limits of separated locally convex spaces. The class of H -spaces contains Frechet spaces and is stable under forming countable inductive and projective limits, closed subspaces and quotient spaces. Moreover, for H -space an unproved variant of the closed graph theorem holds true. Homological methods are used for proving of theorems of vanishing at zero for first derivative of Hausdorff limit functor: Haus 1 (X)=0

Article (eng.) - [pdf] [zip-pdf]

Symmetrical polynomials and conservation laws
Shabat A. B.

Vector fields with symmetrical polynomials as the first integrals are considered. The connection of these dynamical systems with the theory of multi-phase solutions of the solitonic models of mathematical physics is established.

Article (rus.) - [pdf] [zip-pdf]

Nikolai Aleksandrovich Vavilov
(on his 60's anniversary)

Dragilev Mikhail Mikhailovich
(on his 90's anniversary)