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1.
本文利用矩阵论和泛函分析知识,证明了在Hilbert空间中算子迹的Bellman不等式tr(AB)k≤tr(AkBk)当A,B为正迹类算子时,对一切自然数k都成立;当A,B为自伴迹类算子时,对一切偶数k都成立. 相似文献
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Some spectral characterizations of positive operators on Hilbert lattices are pre- sented.The application of these results can yield some equivalent relations of an irreducible positive operator.Some related results for positive operators on Hilbert lattice are also obtained. 相似文献
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Hiroyuki Chihara 《Integral Equations and Operator Theory》2009,63(3):321-335
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex
n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj?strand. We also obtain
the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order
three are in the Wiener algebra of Sj?strand. Our method of proofs is based on the pseudodifferential calculus and the heat
flow determined by the phase function of the Bargmann transform.
Supported by the JSPS Grant-in-Aid for Scientific Research #20540151. 相似文献
5.
设γ:[-1,1]→R~n是R~n中的曲线,沿曲线的γ的Hilbert变换是如下定义的主值积分: Hf(x)=P.V.integral -1 to 1 f(x-γ(t))dt/t,相应的极大算子定义为: Mf(x)=sup 1/h| integral O to h f(x-γ(t))dt|. 对高阶单调曲线本文证明了相应的算子M和H都是L~p(R~n)有界的,从而改进了Nestlerode的结果。 相似文献
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研究了在一些扰动条件下Hilbert广义框架的稳定性,得到了一些结果,这些结果是OLE Christensen关于Hilbert框架经典结果的推广。 相似文献
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A. M. Gomilko 《Functional Analysis and Its Applications》2003,37(1):16-20
Let
be an integer. A Fermat-Euler dynamical system acts on the set of mod-
residues coprime to
by multiplication by a constant (which is also coprime to
). We study the dependence of the period and the number of orbits of this dynamical system on
. Theorems generalizing Fermat's little theorem, as well as empirical conjectures, are given. 相似文献
10.
设H1和H2是两个Hilbert空间,B(H1,H2)表示从H1到H2的所有有界线性算子的集合,T和S分别是H1和H2的两个闭子空间.如果存在线性算子X∈B(H2,H1)满足XAX=X,R(X)=T,N(X)=S,则称X为线性算子A的具有指定像空间T和零空间S的外逆,记为AT,S(2).该文进一步研究了线性算子广义逆AT,S(2)存在的若干等价条件及其性质,建立了算子广义逆AT,S(2)的表示形式. 相似文献
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Hilbert空间中的一类随机算子方程 总被引:3,自引:0,他引:3
本文提出了随机强制算子与随机强单调算子的新概念。研究了在Hilbert空问中一类随机算子方程的随机解。同时推广了著名的Krasnoselkii定理。 相似文献
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本文研究重调和Hardy空间h~2(Ω)上,Toeplitz算子的交换性,给出了h~2(T~2)上一个解析Toeplitz算子与另一个共轭解析Toeplitz算子交换的充分必要条件. 相似文献
14.
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. 相似文献
15.
Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi's results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions. 相似文献
16.
Cai Shi WANG Zhi Yuan HUANG Xiang Jun WANG 《数学学报(英文版)》2005,21(4):787-796
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism. 相似文献
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Let R be a homogeneous ring over an infinite field, IR a homogeneous ideal, and
I an ideal generated by s forms of degrees d
1,...,d
s
so that codim(
:I)s. We give broad conditions for when the Hilbert function of R/
or of R/(
:I) is determined by I and the degrees d
1,...,d
s
. These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S
2 ideals. We prove that the residually S
2 property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property. 相似文献
18.
Operators related to truncated Hilbert transforms on <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> 下载免费PDF全文
Hong Hai Liu 《数学学报(英文版)》2017,33(7):1011-1020
In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H 1 to L 1, and prove variation, oscillation and λ-jump operators related to smooth truncations are bounded from H 1 to L 1. 相似文献
19.
Boundedness of Toeplitz Type Operators Associated to Fractional and Pseudo-Differential Operators on Orlicz Space 下载免费PDF全文
Dazhao Chen 《偏微分方程(英文版)》2021,34(4):297-312
In this paper, the boundedness from Lebesgue space to Orlicz space of certain Toeplitz type operator related to the fractional and pseudo-differential operators
is obtained. 相似文献
20.
The result that for quadratic functions the classical steepest descent algorithm in R
d
converges locally to a two-point attractor was proved by Akaike. In this paper this result is proved for bounded quadratic operators in Hilbert space. The asymptotic rate of convergence is shown to depend on the starting point while, as expected, confirming the Kantorovich bounds. The introduction of a relaxation coefficient in the steepest-descent algorithm completely changes its behaviour, which may become chaotic. Different attractors are presented. We show that relaxation allows a significantly improved rate of convergence. 相似文献