On n-K Width of Certain Function Classes Defined by Linear Op erators in L2 Space

Let M(u) be an N-function, Lr(f, x) and Kr(f, x) are Bak operator and Kan-torovich operator, WM(Lr(f)) and WM(Kr(f)) are the Sobolev-Orlicz classes defined by Lr(f, x), Kr(f, x) and M(u). In this paper we give the asymptotic estimates of the n?K widths dn(WM(Lr(f)),L2[0,1]) and dn(WM(Kr(f)),L2[0,1]).     

Eigenvalues of $$(-\triangle + \frac{R}{2})$$ on manifolds with nonnegative curvature operator

In this paper, we show that the eigenvalues of are nondecreasing under the Ricci flow for manifolds with nonnegative curvature operator. Then we show that the only steady Ricci breather with nonnegative curvature operator is the trivial one which is Ricci-flat.     

Perturbed Dolbeault operators and the homology Todd class

This paper discusses the role played by perturbed Dolbeault operators in relating the coherent sheaf and elliptic operator perspectives on the homology of projective varieties. Among the consequences are index formulas for perturbed Dolbeault operators.

     

象征算子的紧算子逼近算法和逼近速度

传统的微分方程的方法是利用Taylor展开用主象征逼近象征;本文用充分好的紧算子来逼近象征算子,并且逼近算子在算子范数意义下快速逼近原来的算子.     

A Resolution for the Dirac Operator in Four Variables in Dimension 6

The Dirac operator in several operators is an analogue of the - operator in theory of several complex variables. The Hartog’s type phenomena are encoded in a complex of invariant differential operators starting with the Dirac operator, which is an analogue of the Dolbeault complex. In the paper, a construction of the complex is given for the Dirac operator in 4 variables in dimension 6 (i.e. in the non-stable range). A peculiar feature of the complex is that it contains a third order operator. The methods used in the construction are based on the Penrose transform developed by R. Baston and M. Eastwood. The work presented here is a part of the research project MSM 0021620839 and was supported also by the grant GA ČR 201/05/2117.     

Complex powers of degenerate differential operators connected with the Klein-Gordon-Fock operator

We develop a theory of complex powers of the generalized Klein-Gordon-Fock operator

$m^2 - \square - i\lambda \frac{{\partial ^2 }}{{\partial x_1^2 }},\lambda > 0.$

. The negative powers of this operator are realized as potential-type integrals with nonstandard metrics, while positive powers inverse to negative ones are realized as approximative inverse operators.

     

Helton类算子及单值扩张性质

本文研究了Helton类算子在紧摄动下单值扩张性质的稳定性, 同时研究了2×2上三角算子矩阵在紧摄动下单值扩张性质的稳定性. 利用半Fredholm域的特点, 获得了2×2上三角算子矩阵具有单值扩张性质的稳定性的充分必要条件.     

Anti-Wick quantization with symbols in spaces

We give a classification of pseudo-differential operators with anti-Wick symbols belonging to spaces: if the corresponding operator belongs to trace classes; if we get Hilbert-Schmidt operators; finally, if , the operator is compact. This classification cannot be improved, as shown by some examples.

     

粗糙集的矩阵关系

将粗糙集中的集合转化为矩阵刻画,通过引入矩阵算子、类矩阵算子,借助截矩阵和关系矩阵,讨论了Paw lak粗糙集和变精度粗糙集中集合关系的矩阵计算及其所具有的一些基本性质.     

强耗散KDV型方程的指数吸引子

In this paper,we consider the strong dissipative KDV type equation on an unbounded domain R1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space,the existence of exponential attractor in phase space H2（R1） is obtained.     

COMPOSITION OPERATORS ON ANALYTIC VECTOR-VALUED NEVANLINNA CLASSES

Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ： f→foφ on the vector-valued Nevanlinna classes N（X） and Na（X）. Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N（X） and Na（X） if and only if it is weakly compact on the vector-valued Hardy space H^1 （X） and Bergman space B1（X） respectively.     

Compact composition operators on the Smirnov class

We show that a composition operator on the Smirnov class is compact if and only if it is compact on some (equivalently: every) Hardy space for . Along the way we show that for composition operators on both the formally weaker notion of boundedness, and a formally stronger notion we call metric compactness, are equivalent to compactness.

     

张量对称类上诱导线性算子的数值半径

设V是一个n维线性空间,V_x~m(G)为V上的张量对称类.A为V的线性算子T的矩阵,K(A)为V_x~m(G)上的诱导线性算子K(T)的矩阵.本文从K(A)的数值半径Υ(K(A))和可分数值半径Υ_x(K(A))定义出发,研究了Υ(K(A))、Υ_x(K(A))与范数||A||_p(1≤p≤2)、广义矩阵函数d_x~G(A)的关系,得到了它们之间的两个不等式.     

The Boundedness of the Commutator for Riesz Potential Associated with Schr dinger Operator on Morrey Spaces

Let L =-△ + V be the Schr dinger operator on Rd, where △ is the Laplacian on Rdand V≠0 is a nonnegative function satisfying the reverse H lder's inequality.The authors prove that Riesz potential Iβand its commutator [b, Iβ] associated with L map from Mp,qα,vinto Mp1,q1α,v.     

一类非线性算子方程的正算子解的研究

研究了算子方程X^(-1)+A(-1)+A⁺X+X^tA=Q,的正算子解问题,给出了此类非线性算子方程正算子解的范围以及正算子解存在的一些充分必要条件,并用迭代的方法得到了方程的正算子解.     

Phase space universality for multimodal maps

We study the dynamics of the renormalization operator for multimodal maps. In particular, we develop a combinatorial theory for certain kind of multimodal maps. We also prove that renormalizations of infinitely renormalizable multimodal maps with same bounded combinatorial type are exponentially close. Our results imply, for instance, the existence and uniqueness of periodic points for the renormalization operator with arbitrary combinatorial type.     

命题公式集F(S)的基于R0-算子的16类分划

利用R0-蕴涵算子对命题公式集F(S)进行分类,得出了F(S)的—个16类分划,并证明了这种分类关于非运算是同余分类.最后讨论了各类关于MP运算与HS运算的封闭性.     

一类广义有理算子的饱和定理

本文给出了广义有理算子当1＜s≤2时的饱和类.     

单位球的Bergman空间上Schatten类加权复合算子

本文研究了单位球的Bergman空间上Schatten类加权复合算子,得到了这种加权复合算子属于Schatten-Von Neumann.理想S_p的几个充要条件.作为推论给出了Wφ,φ是一个Hilbert- Schmidt算子的充要条件是∫_(Bn)(|ψ(ω)|~2)/((1-|φ(ω)|~2)~(n 1)dV(ω)<∞..     

Mixed modulation spaces and their application to pseudodifferential operators

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients {〈k,Φm,n〉} of certain frame expansions of the kernel k of an integral operator are in ?2,p, then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. Our corollary improves existing Schatten class results for pseudodifferential operators and the corollary is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class.