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型空间上乘法算了,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.     

调和Dirichlet空间上Toeplitz算子与小Hankel算子的交换性

本文研究了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换性的问题.利用算子矩阵表示的方法,获得了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换的充要条件,将Dirichlet空间上的相应结果推广到了调和Dirichlet空间上.     

Dirichlet空间上的紧算子

若S是Dirichlet空间上有限个Toeplitz算子乘积的有限和, S为紧算子的充要条件是: 当z→∂D时, S的Berezin型变换收敛到0; 若S是Dirichlet空间上Hankel算子, S为紧算子的充要条件是: 当z→ D时, S作用在类再生核上按范数收敛到0.     

调和Dirichlet空间上的Toeplitz算子

刻画了调和Dirichlet空间上Toeplitz算子的有界性、紧性,讨论了Toeplitz算子的代数性质,得到了Toeplitz代数与Hankel代数的短正合列.还计算了Toeplitz代数与Hankel代数中Fredholm算子的Fredholm指标,得到了Toeplitz代数与Hankel代数的K_0与K_1群.     

调和Dirichlet空间上小Hankel算子的乘积(英文)

研究了调和Dirichlet空间上调和符号的小Hankel算子的乘积,给出了此类小Hankel算子交换性和乘积为零的完全刻画.     

一类截断Hankel算子的复对称性

截断Hankel算子是Hardy空间上的Hankel算子在模空间上的压缩.该文研究模空间上一类截断Hankel算子的复对称性,给出了完全刻画.所得结果表明,截断Hankel算子的复对称可能仅与模空间有关,也可能与模空间和算子的符号函数均相关.     

Bergman空间上可交换的Hankel算子和Toeplitz算子

证明了Bergman空间上的两个小Hankel算子如果是可交换的且其中一个是拟齐次的小Hankel算子,则另一个也是拟齐次的.还研究了Toeplitz算子和小Hankel算子的交换性.     

Bergman空间L_a~1(D)上的Toeplitz和Hankel算子

本文讨论了Bergman空间L1a(D)中Toeplitz和Hankel算子的w 紧性 ,得到与L2 a(D)上Toeplitz、Hankel算子紧性类似的某些结果     

Hankel算子乘积的两个问题

设f、u和g是单位圆周Hardy空间H2中的函数,h是单位圆周上平方可积的函数,H(f)、Hū、H(g)和Hh都是从单位圆周Hardy空间H2到其正交补空间(H2)⊥上有界的Hankel算子.本文得到了3个Hankel算子的乘积等于一个Hankel算子(即H(f)H*ūH(g)=Hh)成立的充分必要条件,以及H(f)H...     

多重调和Bergman空间上的Toeplitz算子和Hankel算子

完全刻画多重调和Bergman空间上Toeplitz算子和Hankel算子的紧性.运用紧Toeplitz算子这个结果,建立了Toeplitz代数和小Hankel代数的短正合列,推广了单位圆盘上相应的结果.     

On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms

This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.     

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。     

Asymptotic and Partial Asymptotic Hankel Operators on $$H^2(\mathbb{D}^n)$$ H 2 ( D n ) )

In this paper, we generalize the concept of asymptotic Hankel operators on H²(D) to the Hardy space H²(Dⁿ) (over polydisk) in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence. Meanwhile, we introduce i^th-partial Hankel operators on H²(Dⁿ) and obtain a characterization of its compactness for n > 1. Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H²(Dⁿ). It is also shown that a Toeplitz operator with symbol φ is asymptotic Hankel if and only if φ is holomorphic function in L^∞(Tⁿ).     

THE COMPACTNESS OF A KIND OF GENERALIZED HANKEL OPERATORS ON THE BERGMAN SPACE OF THE UNIT BALL

This paper gives the compactness criteria for a kind of generalized Hankel operators on Bergman spaces Lpa(B) defined by M.M.Peloso.     

Dixmier classes on generalized Segal–Bargmann–Fock spaces

We give criteria for the membership of Toeplitz operators and products of Hankel operators, with symbols of a certain type, in the Dixmier class, and formulas for their Dixmier trace, on a variety of weighted Segal–Bargmann–Fock spaces on the complex plane.     

Hankel operators and the Stieltjes moment problem

Let s be a non-vanishing Stieltjes moment sequence and let μ be a representing measure of it. We denote by μn the image measure in Cn of μ⊗σn under the map , where σn is the rotation invariant probability measure on the unit sphere. We show that the closure of holomorphic polynomials in L²(μn) is a reproducing kernel Hilbert space of analytic functions and describe various spectral properties of the corresponding Hankel operators with anti-holomorphic symbols. In particular, if n=1, we prove that there are nontrivial Hilbert-Schmidt Hankel operators with anti-holomorphic symbols if and only if s is exponentially bounded. In this case, the space of symbols of such operators is shown to be the classical Dirichlet space. We mention that the classical weighted Bergman spaces, the Hardy space and Fock type spaces fall in this setting.     

Hankel operators on the Dirichlet space

We study (small) Hankel operators on the Dirichlet space D with symbols in a class of function space, and show that such (small) Hankel operators are closely related to the corresponding Hankel operators on the Bergman space and the Hardy space H².