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Vladikavkaz Mathematical Journal

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January-March, 2003

Volume 5, Issue 1

Issue is dedicated to 50th anniversary of Professor Anatoly Georgievich Kusraev

50th Birthday of Anatoly Georgievich Kusraev
S. S. Goncharov, A. E. Gutman, Yu. L. Ershov, S. S. Kutateladze,
V. L. Makarov, A. M. Nakhushev, Yu. G. Reshetnyak, V. M. Tikhomirov,
G. N. Shotaev

Anatolii Georgievich KusraevFebruary 14, 2003 is the 50th birthday of Professor Anatoly Georgievich Kusraev, a well-knowm specialist in functional analysis.

Anatoly Georgievich Kusraev is a representative of the scientific school of Academician Leonid Vital'evich Kantorovich, an outstanding Soviet mathematician and a Nobel prize winner in economics. His main area of scientific research is functional analysis and its applications.

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

S. S. Kutateladze (Novosibirsk)

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

Approximation by Solutions of Quasielliptical Equations in Lp
M. S. Alborova (Vladikavkaz)
UDC 517.5

The Lp-approximating problem for quasielliptical operators was studied. Some functional geometrical tests are found for a set K to ensure the density of the space η(K) in η p(K) with respect to the Lp-norm.

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

Geometry of Carnot – Caratheodory Spaces, Quasiconformal Analysis, and Geometric Measure Theory
S. K. Vodop'yanov (Novosibirsk)
UDC 517.518.23+517.54+517.813.52+517.954

Some results on geometry of Carnot – Caratheodory spaces are set forth. Application of these results is given to the proof of P-differentiability of Lipschitz mappings and weakly compact mappings of Carnot – Caratheodory spaces. Some applications are also revealed of the theory of differentiability to geometric measure theory and the theory of quasiconformal mappings of Carnot – Caratheodory spaces.

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

Measurable Bundles of C*-algebras
I. G. Ganiev, V. I. Chilin (Tashkent)
UDC 517.98

Let U be a Banach – Kantorovich space over a ring of measurable functions. Let U be a *-algebra and the norm of U have the properties like those of a C*-algebra. We give a representation of U as a mesurable bundle of classical C*-algebras.

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

Optimal Recovery of Derivatives on Sobolev Classes
G. G. Magaril-Il'yaev, K. Yu. Osipenko (Moskow)
UDC 517.51

The problem is considered of optimal recovery of derivatives of functions in Sobolev classes on Rd from inaccurate information on their Fourier transforms. We show that there is a domain Ω0М Rd such that information about the Fourier transform on each domain containing Ω0 leads to no decrease of the optimal recovery error.

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

Optimal Recovery of Analytic Functions by Their Values at an Equidistant Grid on a Circle
K. Yu. Osipenko (Moskow)
UDC 517.51

In the paper an optimal method is constructed of recovery of functions analytic in the unit disk and having the first derivative bounded on using information about the values of these functions at an equidistant grid on the circle |z| = ρ, 0 < ρ < 1.

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

Decomposition of an Atomic Operator
S. N. Tabuev (Vladikavkaz)
UDC 517.98

We prove a theorem on decomposition of an atomic operator in some special basis of lattice homomrphisms and show that this decomposition is in a sense unique.

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

Open Poblems of Nonlinear Dominated Operators in Locally Bounded Spaces of Measurable Functions
V. G. Fetisov (Rostov-na-Dony)
UDC 517.98

We show that to use dominated operators is effective in studying a wide class of operator equations and systems in locally bounded spaces of  Lebesque measurable scalar and vector-valued functions. We also specify some directions of research in which the idea of domination may be rewarding.

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

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