Commutators of Toeplitz Operators On A~p(ψ)

Let denote the positive continous function on ［0,1）. be called normal, if there exist two constants a and b (0＜a＜b) such that (t)(1-t2)a decreases and (t)(1-t2)b increases on ［0,1）. Let dm denote the normalized area measure on the open unit disk D in the complex plane. Define dmp as the measure on D: dmp=p(｜z｜)1-｜z｜2dm(z). For 1p＜∞, let Lp() denote the Banach space of measurable functions f with norm ‖f‖p,φ＝∫D｜f｜pdmpφ1/p＜∞. Ap() denote the closed subspac…     

关于分担多项式的全纯函数的正规族(英文)

In this paper,we study normal families of holomorphic function concerning shared a polynomial.Let F be a family of holomorphic functions in a domain D,k（2）be a positive integer,K be a positive number andα（z）be a polynomial of degree p（p 1）.For each f∈F and z∈D,if f and f sharedα（z）CM and｜f（k）（z）｜K whenever f（z）-α（z）=0 in D, then F is normal in D.     

武汉市2008届高中毕业生二月调研测试理科数学试题

一、选择题(每小题5分,共50分) 　　1.复数z满足方程:z=(z+2)i,则z= 　　A.1+i B.1-i C.-1+i D.-1-i 　　2.在等差数列{an}中,a3=9,a9=3,则a12= 　　A.0 B.3 C.6 D.-3 　　……     

Differential inequalities, normality and quasi-normality

We prove that ifD is a domain in C,α 〉 1 and C 〉 0,then the family F of functions f meromorphic in D such that ｜f′（z）｜/1 ＋ ｜f（z）｜α 〉 C for every z ∈ D is normal in D.For α = 1,the same assumptions imply quasi-normality but not necessarily normality.     

Completeness of the Bergman Metric

In 1921, Bergman introduced the function KD(z, w) =whereis a complete orthonormal system of bounded domain D in Cn. Subsequently,drawing on this function, we can construct the Bergman metric of D. LetTD(z, z) = .Thends = is the Bergman metric of D. Let a(t) = (a1(t), ) a1(t)): [0, 1] -- D be piecewise c1 curve.Suppose that a (t) = . Define the Bergman length of a(t) to be|a|B = [a (t)TD(a(t),a(t))]dt.If z1, z2 E D, define their Bergman (geodesic) distance to bebD(z1, z2) = inf{|a|B|a…     

Bloch型函数的高阶径向导数

讨论了复超球上全纯函数的高阶导数的增长速度 ,证明了f∈Bα 的充分必要条件是supa∈B(1- ｜z｜2 ) m+α- 1｜Rmf(z) ｜ <∞ ,或supa∈B∫B(1-｜z｜2 ) (m+α- 1) ｜Rmf(z) ｜pJRφα(z)dv(z) <∞ ,或 (1- ｜z｜2 ) p(m+α- 1) ｜Rmf(z) ｜pdv(z)是Bergman Carleson测度 .     

新题征展(20)

A　题组新编1 .已知 z∈ C,解下列方程 :( 1 ) z2 - 5| z| 6 =0( 2 ) z| z| - 5z 6 =0( 3) z| z| - 5| z| 6 =0( 4 ) | z2 | - 5| z| 6 =02 .已知棱长为 a的正方体 ABCD -A1B1C1D1,则( 1 )各棱在平面 AB1D1上的射影长之和为 ;( 2 )各棱与平面 AB1D1所成角之和为;( 3)各面在平面 AB1D1上的射影的面积之和为 ;( 4 )各面与平面 AB1D1所成角之和为.3.( 1 )在实数集 R上定义的函数 f( x) ,对任意α,β有f (α) f (β) =f ( α β2 ) f ( α -β2 ) ,且　 f ( 1 ) =2 ,f ( x) 2 ,则满足条件的一个函数是 .( 2 )已知 f ( x)…     

赛题的答案错了吗?

有这样一道竞赛题。已知方程|x|=ax 1有一个负根而且没有正根,那么a的取值范围是( )。 (A)a=1 (B)a>1 (C)a<1 (D)a≥l 给出的答案是:选(D)。我们易发现当a=-0.5时,也满足题意方程有根z=-2.事实上,可解如下: 设a=-0.5,则方程为|z|=-0.5x 1, ∵方程根为负, ∴-x=0.5x十1,解得x=-2。     

一堂解题教学课的实录与启发

在学习了｜a｜-｜b｜≤｜a±b｜≤｜a｜+ ｜b｜之后 ,我精心设计了一堂解题教学课 .在师生的互动活动中 ,教学过程一波三折 ,效果出人意料 ,使我深受启发 .现在对本次课记录如下 ,与大家共享 .出示例题 :求函数f(x) =｜x + 1 ｜-｜x- 2 ｜的最小值经过思考后 ,一位同学提出如下解法 :因为 ｜x+ 1｜≥｜x｜- 1 ①-｜x- 2 ｜≥- ｜x｜- 2 ②所以① +②有 :｜x+ 1｜- ｜x- 2｜≥ 3 ③即　f(x) min =- 3教师评议 :解题思路清楚 .唯一不足的是 :需要指出取“=”的条件 .要使f(x)最小值存在 ,必须③中取得“=” ;③中取得“ =” ,需要①②中“=”…     

On the lower bounds of the curvatures in a bounded domain

Let KD(z,z)be the Bergman kernel of a bounded domain D in Cnand SectD(z,ξ)and RicciD(z,ξ)be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2=TDαβ(z,z)dzαdzβrespectively at the point z∈D with tangent vectorξ.It is proved by constructing suitable minimal functions that SectD(z,ξ)2-2 n+2n+1 KD1(z,z)TD1αβ(z,z)ξαξβKD2(z,z)TD2λμ(z,z)ξλξμ2and RicciD(z,ξ)n+1-(n+2)KD1(z,z)TD1(z,z)ξαξβKD2(z,z)TD2λμ(z,z)ξλξμ,where z∈D1DD2,D1is a ball contained in D and D2is a ball containing D.     

Super-Ergodic operators

The aim of this work is to study operators naturally connected to Ergodic operators in infinite-dimensional Banach spaces, such as Uniform-Ergodic, Cesaro-bounded and Power-bounded operators, as well as stable and superstable operators. In particular, super-Ergodic operators are introduced and shown to be strictly between Ergodic and Uniform-Ergodic operators, and that any power bounded operator is super-Ergodic in a superreflexive space. New relationships between these operators are shown, others are proven to be optimal or can be ameliorated according to structural properties of the Banach space, such as the superreflexivity or with unconditional basis.

     

Unitary equivalence of one-parameter groups of Toeplitz and composition operators

The composition operators on H² whose symbols are hyperbolic automorphisms of the unit disk fixing ±1 comprise a one-parameter group and the analytic Toeplitz operators coming from covering maps of annuli centered at the origin whose radii are reciprocals also form a one-parameter group. Using the eigenvectors of the composition operators and of the adjoints of the Toeplitz operators, a direct unitary equivalence is found between the restrictions to zH² of the group of Toeplitz operators and the group of adjoints of these composition operators. On the other hand, it is shown that there is not a unitary equivalence of the groups of Toeplitz operators and the adjoints of the composition operators on the whole of H², but there is a similarity between them.     

A Study of Probability Measures Through Commutators

The first-order moments and two families of commutators are proven to determine uniquely the moments of a probability measure on ℝ ^d . These families are the commutators between the annihilation and creation operators, and the commutators between the annihilation and preservation operators. An explicit method for recovering the moments from these commutators and first-order moments is presented.      

Essentially subnormal operators

An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form ``normal plus compact'.

The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam's Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.

     

Dirichlet型空间上Hankel算子和乘法算子

本文讨论了Dirichlet型空间上的再生核,并对Dirichlet型空间上乘法算子,Hankel算子和小Hankel算子的基本性质进行了研究,同时也给出了这些算子的有界性,紧性和Schatten理想的初步刻画。     

加权Bergman空间上的Toeplitz算子和Hankel算子

西方给出了Ｃ＾ｎ中单位球上的带权的Ｂｅｒｇｍａｎ空间上具一般符号的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧的充要条件。     

映人E0(p,q)的紧复合算子

应用复合算子研究E0（p,q）空间,当p=2时,它就是Qq,0,当P>0且q>1时,它就是小 Bloch空间B0.讨论了复合算子的紧性并利用Carleson测度给出复合算子是紧的判别准则.     

加权Morrey-Herz空间上的广义Hausdorff算子

引入了一种新的广义Hausdorff算子.它包括了许多著名的算子作为其特殊情形.我们得到了这些算子在加权Morrey-Herz空间上有界的充分必要条件,还得到了相应的新的算子范数不等式.它们是许多著名结果有意义的改进和推广.     

Composition operators on Hardy spaces of a half-plane

We consider composition operators on Hardy spaces of a half-plane. We mainly study boundedness and compactness. We prove that on these spaces there are no compact composition operators.

     

Disturbing Fuzzy Propositional Logic and its Operators

In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The properties of these logic operators are studied.