Volume 14, Issue 1

This issue is dedicated to the memory of Academician
Leonid V. Kantorovich (19.01.1912 - 07.04.1986), Laureate of the Stalin, Lenin
and Nobel Prizes.

Signposts of the Life
of Leonid V. Kantorovich

Mathematics and Economics in the Legacy
of Leonid Kantorovich
Kutateladze S. S.

This is a short overview of the life of Leonid Kantorovich and his contribution to the formation of the modern outlook on the interaction between mathematics and economics.

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

Optimal recovery of a harmonic function from inaccurate information on the values of the radial integration operator
Bagramyan T.

We consider the problem of optimal recovery of a harmonic function in the unit ball from the inaccurate values of the radial integration operator. Information on the values of the operator is given as a function that differs from the exact values in the mean-square metric not more than a fixed error, either in the form of a finite set of Fourier coefficients calculated with a fixed error in the mean square or uniform metric.

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

On ergodic properties of homogeneous Markov chains
Golovneva E. V.

In this paper we continue our investigations initiated in [1]. Namely, we study the spectrum of Kolmogorov matrices with at least one column separated from zero. It is shown that λ=0   is an eigenvalue with multiplicity 1, while the rest of the spectrum is separated from zero. Therefore, a Markov process generated by such a matrix converges to its uniquely defined final distribution exponentially fast. We give an explicit estimate for the rate of this convergence.

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

An example of using Δ 1   terms in boolean valued analysis
Gutman A. E.

Syntactic tools related to Δ 1   terms are demonstrated by application to Boolean valued analysis. As an example, the question is considered of what approaches to defining the field ℝ   of reals and what complete Boolean algebras B   provide the explicit inclusion ℝ^ ⊂ℝ   inside the Boolean valued universe V (B) .

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

Some remarks on zeros of one class of harmonic functions
Korobeinik Yu. F.

It is shown that under some additional restrictions the method of the paper [1] is applicable to a case that was left open.

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

Kantorovich's principle in action: A W * -modules and injective Banach lattices
Kusraev A. G.

Making use of Boolean valued representation it is proved that Kaplansky-Hilbert lattices and injective Banach lattices may be produced from each other by means of the convexification procedure. The relationship between the Kantorovich's heuristic principle and the Boolean value transfer principle is also discussed.

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

Extension of an almost f -algebra multiplication
Chil E.

It is proved that an almost f -algebra multiplication and a d -algebra multiplication defined on a majorizing vector sublattice of a Dedekind complete vector lattice can be extended to the whole vector lattice by using purely algebraic and order theoretical means.

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