On distributionally regenerative processes

The paper is concerned with characterization results for distributional regeneration. It is shown that distributional regeneration is equivalent to renewal representation of the associated (shift) Markov operator. A sufficient condition for the distributional regeneration of the transfer operator in terms of variation is also formulated. Finally, a minorization condition is formulated and proved to be sufficient for recurrent co-Feller operators.     

沿高阶单调曲线的Hilbert变换和极大算子的L^p估计

设γ:[-1,1]→R~n是R~n中的曲线,沿曲线的γ的Hilbert变换是如下定义的主值积分: Hf(x)=P.V.integral -1 to 1 f(x-γ(t))dt/t,相应的极大算子定义为: Mf(x)=sup 1/h| integral O to h f(x-γ(t))dt|. 对高阶单调曲线本文证明了相应的算子M和H都是L~p(R~n)有界的,从而改进了Nestlerode的结果。     

FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

ＦＩＸＥＤＰＯＩＮＴＳＡＮＤＣＯＵＰＬＥＤＦＩＸＥＤＰＯＩＮＴＳＦＯＲＩＮＣＲＥＡＳＩＮＧＯＰＥＲＡＴＯＲＳＷＩＴＨＡＰＰＬＩＣＭＩＯＮＳＴＯＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺＨＡＮＧＳＨＩＳＨＥＮＧＡＮＤＨＵ...     

OnM-ideals and best approximation

In this paper we will prove some theorems on theM-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].This work is supported in part by the National Natural Science Foundation of China.     

A NEW LAPLACIAN COMPARISON THEOREM AND THE ESTIMATE OF EIGENVALUES

This paper establishes a new Laplacian comparison theorem which is specially useful to the manifolds of nonpositive curvature.It leads naturally to the corresponding heat kernel comparison and eigenvalue comparison theorems. Furthermore, a lower estimate of L^2-spectrum of an n-dimensional non-compact complete Cartan-Hadamard manifold is given by (n-1)k/4,provided its Ricci curvature ≤-(n-1)k(k=const.≥0).     

The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator

Abstract The existence of infinitely many solutions to Sturm-Liouville boundary value problem with aLaplacian-like operator is studied by applying generalized polar coordinates.     

在白噪声分析中的广义维里拉普拉斯

一类广义维里拉普拉斯，把在白噪声分析构架中通常定义的维里拉普拉斯作为特殊情形而包含。     

On the Spectral Multiplicity of Some Volterra Operators in Sobolev Spaces

Mathematical Notes -     

Preconditioning the Poincaré-Steklov operator by using Green's function

This paper is concerned with the Poincaré-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the Poincaré-Steklov operator can be expressed explicitly by an integral operator with a kernel being the Green's function restricted to the interface. As an application, for the discrete Poincaré-Steklov operator with respect to either a line (edge) or a star-shaped web associated with a single vertex point, a preconditioner can be constructed by first imbedding the line as the diameter of a disk, or the web as a union of radii of a disk, and then using the Green's function on the disk. The proposed technique can be effectively used in conjunction with various existing domain decomposition techniques, especially with the methods based on vertex spaces (from multi-subdomain decomposition). Some numerical results are reported.

     

Generalized indices of operators inB(H)

A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so that the operations: ∞ ± n = ∞, ∞ + ∞ = ∞, which used to play an inflexible role, are refined and moreover, ∞ - ∞, which used to be meaningless, is done in sense. Then generalized index for semi-Fred-holm operators is developed to wholeB(H), i.e. all of bounded linear operators in Hilbert spaceH. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form, practically a refined result of the known proposition. Then, it is proved thatB(H) is the union of countably many disjoint arewise connected sets over all the generalized dimensions ofB(H). Project supported by the National Natural Science Foundation of China