On an Embedding Criterion for Interpolation Spaces and Application to Indefinite Spectral Problems

An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L _2,g space of eigenfunctions of an indefinite Sturm–Liouville problem u=gu on the interval (-1,1) with the Dirichlet boundary conditions, provided that the function g(x) changes sign at the origin. In particular, the basis property criterion is established for an odd g(x). Some connections with stability in interpolation scales are discussed.     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .

     

THE SPACE—FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS

The space-fractional telegraph equation is analyzed and the Fourier transform of its fundamental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies the space-fractional telegraph equation, is presented. Its limiting behaviour and the connection with symmetric stable processes is also examined.     

An improvement of the Kolmogorov–Riesz compactness theorem

The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical result by Kolmogorov–Riesz on compact subsets of Lebesgue spaces.     

A capacitary weak type inequality for Sobolev functions and its applications

In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.

     

Rolling of a non-homogeneous ball over a sphere without slipping and twisting

Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, J. Koiller and K. Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.      

一类Block型李代数的分类和中心扩张

本文我们决定了一类Block型李代数$\BB$在同构意义下的分类和中心扩张, 其中$q$是一个非零复数. 我们的结果推广了以前的一些结果.     

Principal values for Riesz transforms and rectifiability

Let E⊂Rd with Hn(E)<∞, where Hn stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit

     

带参数2n 阶非对称微分算子的一些线性同构定理

本文给出了一类带参数２ｎ阶非对称微分算子Ａ_λ的一些正则性定理，籍此可刻画一类飞行器在其运行过程中的双向平稳行为．