October  December, 2012
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.
Article (rus.)  [pdf] [zippdf]
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
nonelliptic case, when their symbols degenerate on a set
of measure zero. The ranges of these operators are also described.
Article (rus.)  [pdf] [zippdf]
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 highfrequency 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] [zippdf]
The asimptotics of conditionally periodic solution
of differential equation containing great highfrequency terms
Ishmeev M. R.
It was constructed and justified the full asimptotic
of conditionally periodic solution for the systems of nonlinear
differential equations containing items proportional to some degrees of frequency.
Article (rus.)  [pdf] [zippdf]
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] [zippdf]
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] [zippdf]
On Maharam polynomials
Kusraeva Z. A., Tasoev B. B.
A RadonNikodym type theorem is proved and the Maharam extension
is constructed for positive orthogonally additive polynomials in vector lattices.
Article (rus.)  [pdf] [zippdf]
On correlation of two solution classes for NavierStokes 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 NavierStokes 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] [zippdf]
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] [zippdf]
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] [zippdf]
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 multiphase solutions of the solitonic models of
mathematical physics is established.
Article (rus.)  [pdf] [zippdf]
Nikolai Aleksandrovich Vavilov
(on his 60's anniversary)
Article (rus.)  [pdf] [zippdf]
Dragilev Mikhail Mikhailovich
(on his 90's anniversary)
Article (rus.)  [pdf] [zippdf]
