基于模糊集值映射的粗糙近似算子

给出基于模糊集值映射F的模糊集的下(上)近似等概念,研究F-下(上)近似算子aprF(aprF)的性质,探讨求它们的方法,得到若干结果.     

Methods for wave equation prestack depth migration and numerical experiments

In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical re-     

随机算子方程随机解的若干存在性定理

自提出随机拓扑度和随机不动点指数概念以来,随机拓扑度和随机不动点指数理论已成为研究随机非线性算子的一种基本方法,建立了许多新的定理。利用随机不动点指数理论,研究了不同边界条件下的随机算子方程随机解的存在性,得到了若干新的结果,所得结果推广了相关文献中的部分结果     

Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces

Let ψ be a holomorphic function on the open unit disk D and φ a holomorphic self-map of D. Let C_φ,M_ψ and D denote the composition, multiplication and differentiation operator, respectively. We find an asymptotic expression for the essential norm of products of these operators on weighted Bergman spaces on the unit disk. This paper is a continuation of our recent paper concerning the boundedness of these operators on weighted Bergman spaces.     

鞅的矩型极大算子的若干不等式

给出了算子T=∑_(n=1)~∞T_n在H_B~p和BMO_(p,B)~-上有界的一些充分条件,其中T_n(n∈P)为具有Δ性质的算子.作为应用,借助于算子值鞅变换得到了关于鞅的矩型极大算子的强(p,p)型不等式和弱(1,1)型不等式,以及其在BMO_(p,B)~-上的有界性.这些结果与经典H~p鞅论中极大算子的性质相对应.     

Weighted composition operators on the Hilbert space of Dirichlet series

In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.     

The characteristic of noncompact convexity and random fixed point theorem for set-valued operators

Let (Ω, Σ) be a measurable space, X a Banach space whose characteristic of noncompact convexity is less than 1, C a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C. We prove that a set-valued nonexpansive mapping T: C → KC(C) has a fixed point. Furthermore, if X is separable then we also prove that a set-valued nonexpansive operator T: Ω × C → KC(C) has a random fixed point.     

On sign-changing solutions for nonlinear operator equations

In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations.     

On products of unbounded operators

A symmetric operator X^ is attached to each operator X that leaves the domain of a given positive operator A invariant and makes the product AX symmetric. Some spectral properties of X^ are derived from those of X and, as a consequence, various conditions ensuring positivity of products of the form AX ₁ ... X _n are proved. The question of ^-complete positivity of the mapping p → Ap(X ₁,...,X _n) defined on complex polynomials in n variables is investigated. It is shown that the set ω is related to the McIntosh-Pryde joint spectrum of (X ₁,...,X _n) in case all the operators A, X ₁,...,X _n are bounded. Examples illustrating the theme of the paper are included. This revised version was published online in June 2006 with corrections to the Cover Date.