On the asymptotics of some systems of difference equations

We prove an inclusion theorem regarding a system of difference equations and apply it in getting the asymptotics of some solutions of some concrete difference equations.     

On the pointwise ergodic behaviour of transformations preserving infinite measures

We consider situations in which the asymptotic type of a measure preserving transformation manifests itself in a pointwise manner.     

On value preserving and growth optimal portfolios

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with the minimal martingale measure only for complete markets.     

On the intersection of infinite matroids

We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by Aharoni and Berger in 2009.We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids.In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays.     

On the associativity of the product of measure spaces

If we arbitrarily choose finitely many measure spaces, then the existence of a product of these measure spaces can be proved. It is well known that this operation is not associative which is a substantial difficulty. In this paper we show that the associative law remains true between the σ-algebras of the product spaces, and we give an extension of the Fubini's theorem. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the asymptotics of the spectrum of a nonsemibounded vector Sturm-Liouville operator

On the half-line, we consider a vector Sturm-Liouville operator with a potential that is unbounded below. Asymptotic formulas for the spectrum are given. These formulas involve the eigenvalues of the matrix potential as well as the “rotational velocities” of the eigenvectors.     

On the dimension of infinite covers

We prove the following theorem and some generalizations. . Let be a connected CW complex which satisfies Poincaré duality of dimension . For any subgroup of , let denote the cover of corresponding to . If has infinite index in , then is homotopy equivalent to an -dimensional CW complex.

     

On the local asymptotics of Faber polynomials

We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.

     

A characterization of Möbius transformations

Let be an integer and let be a domain of . Let be an injective mapping which takes hyperspheres whose interior is contained in to hyperspheres in . Then is the restriction of a Möbius transformation.

     

Logarithmic asymptotics of solutions of the large deviation problem for the boltzmann equation with small transfer of momentum

For the Boltzmann equation with small transfer of momentum, we derive a system of nonlinear integral-differential equations describing the logarithmic asymptotics of the solution to the Cauchy problem in the domain at the distanceO(1) from the support of the initial condition.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 73–94, July, 1998.This research was partially supported by INTAS-RFBR under grant No. 95-91 in the case of the first author, and by INTAS under grant No. 96-0698 in the case of the second author.     

The leading term of the spectral asymptotics for the Kohn-Laplace operator in a bounded domain

We prove the Weyl asymptotic formula for the number of eigenvalues of the Kohn-Laplace operator on a Heisenberg group and write out the leading term of asymptotics. The method of study is based on estimates of the Green function for the Dirichlet problem for the corresponding parabolic operator and makes use of the classical Hardy-Littlewood Tauberian theorem.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 493–505, October, 1998.This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00443 and No. 96-01-00503.     

遍历定理的应用--一类极限的求法

作为遍历理论的应用,讨论一类极限的求法.     

On the Ranks of Certain Semigroups of Orientation Preserving Transformations

We classify the unmixed squarefree lexsegment ideals and determine those which are Cohen–Macaulay.     

非Lipschitz仿射映射的半拓扑半群的强遍历定理(英)

本文在Banach空间中给出了非Lipschitzian仿信射拓扑半群的强遍历定理。     

On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distributions

We study the distribution of the maximum M of a random walk whose increments have a distribution with negative mean which belongs for some γ > 0 to a subclass of the class S _γ (for example, see Chover, Ney, and Wainger [5]). For this subclass we provide a probabilistic derivation of the asymptotic tail distribution of M and show that the extreme values of M are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the “spatially local” asymptotics of the distribution of M, the maximum of the stopped random walk for various stopping times, and various bounds.