Fock空间上径向函数诱导的Toeplitz算子

本文讨论了Fock空间上以径向函数和拟齐次函数为符号的Toeplitz算子的代数性质,给出了两个以径向函数为符号的Toeplitz算子的积仍为Toeplitz算子的充分必要条件,并且研究了以拟齐次函数为符号的Toeplitz算子的交换性.     

单位多圆柱上Bergman空间中的分别准齐次ToePlitz算子

本文研究了单位多圆柱上Bergman空间中以分别准齐次函数为记号的Toeplitz算子的代数性质.我们首先得到了两个以分别准齐次函数为记号的Toeplitz算子可以写成一个Toeplitz算子的充分必要条件,然后利用L2(Dn,dV)的一个极分解式证明了,只要其中有一个Toeplitz算子是分别准齐次的,则其零乘积问题...     

Bergman空间上拟齐次Toeplitz算子的乘积

使用Mellin变换作为工具,讨论了Bergman空间上以拟齐次函数为符号的Toeplitz算子的乘积问题,得出了当拟齐次函数的度处于三种不同情况时两个Toeplitz算子乘积仍是Toeplitz算子的充分必要条件.     

Dirichlet空间上Toeplitz算子与Berezin型变换相关的一些性质

本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2T_uv-T_uT_v-T_vT_u 的紧性, 其中函数u,v ∈ L^2,1.     

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.     

Dirichet空间上Toeplitz算子的若干问题

讨论了Dirichlet空间上Toeplitz算子的紧性,特别地得到了Schatlen类Toeplitz算子的特征.此外,还证明了关于Toeplitz算子的一个非稠密性定理,并证明一个非零的函数可以诱导一个零算子,这与Hardy空间及Bergman空间情形是一重大差别.     

加权Dirichlet空间上具有无界符号的Toeplitz算子(英文)

本文研究了加权Dirichlet空间上一类Toeplitz性质的问题.利用构造单位圆盘D上一类无界函数的方法,获得了以它为符号的Toeplitz算子是紧的结果.同时也通过构造一类L2(?)上的函数,使得它们在单位圆周上每一点的任何一个邻域都无界的方法,获得了以这些函数为符号的Toeplitz算子是迹类算子的结果.     

Diricher空间上Toeplitz算子的若干问题

讨论了Dirichlit空间上Toeplitz算子的紧性,特别地得到了Schatlen类Toeplitz算子的特征,此外,还证明了关于Toeplitz算子的一个非稠密性定理,并证明一个非零的函数可以诱导一个零算子,这与Hardy空间及Bergman空间情形是一重大差别。     

离散交换群上Toeplitz 算子的代数性质

广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果.     

一类拟线性椭圆方程径向整体正解的分类性质 献给余家荣教授100华诞

本文对如下拟线性方程整体径向正解进行分类研究:{r~(-γ)(r~α|u′|~βu′)′+|u|~(p-1)u=0, 0 r ∞,u(0)=ρ 0, u′(0)=0.这类方程中的微分算子包含了径向函数空间中通常的Laplace算子、m-Laplace算子和k-Hessian算子.本文研究该类方程的任意两个解(包括奇异解)之间的相交和分离的性质,完整地给出各种情形下它们之间的相交数,解决了Miyamoto (2016)未解的一种情形.     

Positivity of Fock Toeplitz Operators via the Berezin Transform

This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z) = a + be~(-α|z|~2)+ ce~(-β|z|~2), where a, b, c are real numbers and α, β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of φ is a nonnegative function on the complex plane, but the corresponding Toeplitz operator Tφ is not positive on the Fock space.     

Commutants of Toeplitz operators with radial symbols on the Fock–Sobolev space

In the setting of the Fock space over the complex plane, Bauer and Lee have recently characterized commutants of Toeplitz operators with radial symbols, under the assumption that symbols have at most polynomial growth at infinity. Their characterization states: If one of the symbols of two commuting Toeplitz operators is nonconstant and radial, then the other must be also radial. We extend this result to the Fock–Sobolev spaces.     

Radial Toeplitz Operators on the Fock Space and Square-Root-Slowly Oscillating Sequences

In this paper we show that the C*-algebra generated by radial Toeplitz operators with \(L_{\infty }\)-symbols acting on the Fock space is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric \(\rho (j,k)=|\sqrt{j}-\sqrt{k}\,|\). More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.     

Toeplitz Operators on the Fock Space

We study Toeplitz operators on the Fock space with positive measures as symbols. Main results include characterizations of Fock–Carleson measures, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten p-classes.     

Carleson Measures and Toeplitz Operators on Doubling Fock Spaces

Given φ a subharmonic function on the complex plane C,with ?φdA being a doubling measure,the author studies Fock Carleson measures and some characterizations onμsuch that the induced positive Toeplitz operator T_μ is bounded or compact between the doubling Fock space F_φ~p and F_φ~∞ with 0p≤∞,where μ is a positive Borel measure on C.     

Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.     

Commuting Toeplitz operators on the Segal-Bargmann space

Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily.     

Toeplitz Operators on Arveson and Dirichlet Spaces

We define Toeplitz operators on all Dirichlet spaces on the unit ball of and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. The research of the second author is partially supported by a Fulbright grant.     

A^p（φ）上Toeplitz算子的换位子

本文使用不变加权面积平均值性质刻画了单位圆盘内的调和函数．由此我们探讨了加权Bergman空间A^p(φ)上的Toeplitz算子，给出了两个具有界调和符号的Toeplitz算子交换或本质交换的一些充要条件．