多圆柱上Dirichlet空间中Toeplitz算子的交换性

本文讨论了多圆柱上Dirichlet空间中的正规Toeplitz算子以及全纯指标和反全纯指标的两个Toeplitz算子的交换性.我们证明具有多圆柱上Dirichlet空间中反全纯指标的两个Toeplitz算子可交换当且仅当两个指标是线性相关的,同时证明全纯指标和反全纯指标的两个Toeplitz算子可交换当且仅当两个指标有一个是常数.     

Eigenvalues and Spectra of Composition Operators Acting on Weighted Bergman Spaces of Infinite Order on the Unit Polydisk

We give the spectra of bounded composition operators acting on the weighted Bergman spaces of infinite order on the unit polydisk defined for a weight v which is radial in each component, when the symbol of the operator has a fixed point in the unit polydisk.     

多圆盘Bergman空间上Toeplitz算子的乘积和交换性

该文给出了多圆盘Bergman空间上两个带有某种符号的Toeplitz算子的乘积等于另一个Toeplitz算子的充分必要条件,并且给出了乘积算子所带符号的公式.接下来,相应的研究了它的交换性.这些研究结果都是根据符号函数的Mellin变换.     

Zero Products of Toeplitz Operators with <Emphasis Type="Italic">n</Emphasis>-Harmonic Symbols

On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products with four factors. We also prove a local version of this result for products with three factors.     

Finite rank Toeplitz products with harmonic symbols

On the Bergman space of the unit ball of Cn, we study the finite rank problem for Toeplitz products with harmonic symbols. We first solve the problem with two factors in case symbols have local continuous extension property up to the boundary. Also, in case symbols have additional Lipschitz continuity up to (some part of) the boundary, we solve the problem for multiple products with number of factors depending on the dimension n. Analogous theorems on the polydisk are also obtained.     

单位多圆盘加权Bergman空间上Toeplitz算子的本质谱

本文研究了单位多圆盘加权Bergman空间AΦp(Dn)上的Toeplitz算子.利用多圆盘函数论,获得了L∞(Dn)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱.     

Schwarz-Pick estimates for holomorphic mappings from the polydisk to the unit ball

In this paper, Schwarz-Pick estimates of arbitrary order partial derivatives for holomorphic mappings from the polydisk to the unit ball are presented. We generalize the early work on Schwarz-Pick estimates of higher order derivatives for bounded holomorphic functions on the unit disk and the polydisk.     

Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality

We obtain a decomposition for multivariable Schur-class functions on the unit polydisk which, to a certain extent, is analogous to Agler's decomposition for functions from the Schur-Agler class. As a consequence, we show that d-tuples of commuting strict contractions obeying an additional positivity constraint satisfy the d-variable von Neumann inequality for an arbitrary operator-valued bounded analytic function on the polydisk. Also, this decomposition yields a necessary condition for solvability of the finite data Nevanlinna-Pick interpolation problem in the Schur class on the unit polydisk.     

Hardy Spaces of Dirichlet Series and Their Composition Operators

 In [9], Hedenmalm, Lindqvist and Seip introduce the Hilbert space of Dirichlet series with square summable coefficients , and begin its study, with modern functional and harmonic analysis tools. The space is an analogue for Dirichlet series of the space for Fourier series. We continue their study by introducing , an analogue to the spaces . Thanks to Bohr’s vision of Dirichlet series, we identify with the Hardy space of the infinite polydisk . Next, we study a variant of the Poisson semigroup for Dirichlet series. We give a result similar to the one of Weissler ([25]) about the hypercontractivity of this semigroup on the spaces . Finally, following [8], we determine the composition operators on , and we compare some properties of such an operator and of its symbol. Received October 3, 2001; in revised form January 16, 2002 Published online July 12, 2002     

Schur–Agler and Herglotz–Agler classes of functions: Positive-kernel decompositions and transfer-function realizations

We discuss transfer-function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit disk or the right halfplane (Schur/Herglotz functions over either the unit polydisk or the right polyhalfplane) which satisfy the appropriate stronger contractive/positive real part condition for the values of these functions on commutative tuples of strict contractions/strictly accretive operators (Schur–Agler/Herglotz–Agler functions over either the unit polydisk or the right polyhalfplane). As originally shown by Agler, the first case (polydisk to disk) can be solved via unitary extensions of a partially defined isometry constructed in a canonical way from a kernel decomposition for the function (the lurking-isometry method). We show how a geometric reformulation of the lurking-isometry method (embedding of a given isotropic subspace of a Kre?n space into a Lagrangian subspace—the lurking-isotropic-subspace method) can be used to handle the second two cases (polydisk to halfplane and polyhalfplane to disk), as well as the last case (polyhalfplane to halfplane) if an additional growth condition at ∞ is imposed. For the general fourth case, we show how a linear-fractional-transformation change of variable can be used to arrive at the appropriate symmetrized nonhomogeneous Bessmertny? long-resolvent realization. We also indicate how this last result recovers the classical integral representation formula for scalar-valued holomorphic functions mapping the right halfplane into itself.     

多元盘Bergman空间上可逆的Toeplitz算子乘积

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

Bessel fusion multipliers

In this paper we study properties of a Bessel multiplier when the symbol involved belongs to lp. Furthermore, we introduce the concept of Bessel fusion multiplier which generalizes a Bessel multiplier for Bessel fusion sequences. We study their behavior when the symbol belongs to lp and some continuity properties.     

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.     

Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.     

多圆盘的Bergman空间上Hankel乘积

对多圆盘上的平方可积函数f和g,研究了Bergman空间上稠密定义的Hankel乘积H_fH_g~*的有界性和紧性.给出了这些算子有界和紧的一些必要条件和充分条件.当f是解析函数时,对混合Haplitz乘积H_gT_(f~-)和T_fH_g~*得到了相似的结果.     

m-Berezin Transform on the Polydisk

m-Berezin transforms are introduced for bounded operators on the Bergman space of the polydisk. We show several properties of m-Berezin transform and use them to show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the polydisk. A useful and sharp approximate identity of its m-Berezin transforms is obtained for a bounded operator.     

A Schwarz lemma on the polydisk

We prove a generalization of the infinitesimal portion of the classical Schwarz lemma for functions from the polydisk to the disk. In particular, we describe the functions which play the role of automorphisms of the disk in this context-they turn out to be rational inner functions in the Schur-Agler class of the polydisk with an added symmetry constraint. In addition, some sufficient conditions are given for a function to be of this type.

     

多圆盘上的本质交换对偶Toeplitz算子

在单位多圆盘的Bergman空间上,本文分别刻画了以有界可测函数和有界多重调和函数为符号的本质交换对偶Toeplitz算子.