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Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system

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Science China Mathematics 2021年第2期64卷 351-372页

作者： Youfa Li deguang han Shouzhi Yang Ganji Huang College of Mathematics and Information Science Guangxi UniversityNanning 530004China Department of Mathematics University of Central FloridaOrlandoFL 32816USA Department of Mathematics University of ShantouShantou 535063China

The Sobolev space H^(■)(R^(d)),where■>d/2,is an important function space that has many applications in various areas of *** to the inertia of a measurement instrument,it is desirable in sampling theory to recover a function by its nonuniform *** the present paper,based on dual framelet systems for the Sobolev space pair(H^(s)(R^(d)),H^(-s)(R^(d))),where d/2

关键词： Sobolev space framelet series truncation error perturbation error nonuniform sampling and approximation

Structural Properties of Homomorphism Dilation Systems

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Chinese Annals of Mathematics,Series B 2020年第4期41卷 585-600页

作者： deguang han David R.LARSON Bei LIU Rui LIU Department of Mathematics University of Central FloridaOrlando 32816USA. Department of Mathematics Texas A&M UniversityCollege Station 77843USA. School of Science Tianjin University of TechnologyTianjin 300384China. Corresponding author.School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071China.

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras,the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector *** introducing two natural dilation structures,namely the canonical and the universal dilation systems,they prove that every linearly minimal dilation is equivalent to a reduced homomorphism dilation of the universal dilation,and all the linearly minimal homomorphism dilations can be classified by the associated reduced subspaces contained in the kernel of synthesis operator for the universal dilation.

关键词： Linear systems Linearly minimal homomorphism dilation systems Principle and universal dilations Equivalent dilation systems

Operator valued frames and structured quantum channels

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Science China Mathematics 2011年第11期54卷 2361-2372页

作者： han deguang LI PengTong MENG Bin TANG WaiShing Department of Mathematics University of Central Florida Orlando FL 32816 USA Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 China Department of Mathematics National University of Singapore Singapore 119076 Singapore

Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on developing the theory about operator-valued frame generators for projective unitary representations of finite or countable groups which can be viewed as the theory of quantum channels with group structures. We present new results for operator-valued frames concerning (general and structured) dilation property, orthogonal frames, frame representation and dual frames. Our results are complementary to some of the recent work of Kaftal, Larson and Zhang, and in some cases our treatment is more elementary and transparent.

关键词： operator-valued frames quantum channels Parseval duals projective unitary representation

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 227-236页

作者： han deguang Department of Mathematics, Qufa Normal University, Qufu 273165, Shandong, China. Department of Mathematics Qufa Normal University Qufu 273165 Shandong China

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0+ (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.

关键词： Nest algebra Derivation Continuity Linearity Banach space

Constructing super Gabor frames:the rational time-frequency lattice case

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Science China Mathematics 2010年第12期53卷 3179-3186页

作者： LI ZhongYan 1 & han deguang 2, 1 Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA Department of Mathematics and Physics North China Electric Power University Beijing China Department of Mathematics University of Central Florida Orlando USA

For a time-frequency lattice Λ = A Z d × B Z d , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if |det( AB) | = 1 L . The proof of this result involves various techniques from multi-lattice tiling and operator algebra theory, and it is far from constructive. In this paper we present a very general scheme for constructing super Gabor frames for the rational lattice case. Our method is based on partitioning an arbitrary fundamental domain of the lattice in the frequency domain such that each subset in the partition tiles R d by the lattice in the time domain. This approach not only provides us a simple algorithm of constructing various kinds of orthonormal super Gabor frames with flexible length and multiplicity, but also allows us to construct super Gabor (non-Riesz) frames with high order smoothness and regularity. Several examples are also presented.

关键词： super Gabor frame orthonormal super frame full rank lattice tiles

140m至170m超高层住宅消防系统转输供水设计探讨

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给水排水 2023年第8期49卷 81-86页

作者：谭斌韩德广田波中交第二公路勘察设计研究院有限公司武汉430056 中建三局第一建设工程有限责任公司武汉430040 基准方中建筑设计股份有限公司成都610093

针对140~170 m超高层住宅消防系统转输供水设计,分析了水泵直接串联系统、消防水泵+转输水箱串联系统(避难层)、消防水泵+转输水箱串联系统(屋面)这三种消防系统转输供水方案的优缺点,并以工程实例分析了消防水泵+转输水箱串联系统(屋面... 详细信息

针对140~170 m超高层住宅消防系统转输供水设计,分析了水泵直接串联系统、消防水泵+转输水箱串联系统(避难层)、消防水泵+转输水箱串联系统(屋面)这三种消防系统转输供水方案的优缺点,并以工程实例分析了消防水泵+转输水箱串联系统(屋面)的实际工程应用。

关键词：超高层住宅消防系统转输供水

Derivations and Isomorphisms of Certain Reflexive Operator Algebras

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Acta Mathematica Sinica,English Series 1998年第1期14卷 105-112页

作者： Hou Chengjun han deguang Department of Mathematics, Qufu Normal University, Qufu 273165, China Institute of Mathematics, Fudan University, Shanghai 200433, China Department of Mathematics, Qufu Normal University, Qufu 273165, China 曲阜师范大学数学系山东曲阜

In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.

关键词： CDS algebra Nest algebra Derivation Isomorphism

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一个最佳逼近定理与拟三角算子空间

曲阜师范大学学报(自然科学版) 1987年第4期 144-147页

作者：韩德广

本文证明了弱算子拓扑闲空间的一个最佳逼近结果,并相应地得到了拟三角算子空间的最佳逼近定理.文〔1〕中的结果是本文结果的特殊情形.

关键词：拟三角算子逼近定理弱算子拓扑最佳逼近元有限秩强拓扑向量拓扑

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向量空间和C^(*)-代数上的扩张理论

曲阜师范大学学报（自然科学版） 2022年第3期48卷 23-32页

作者：包琪瑶韩德广刘锐南开大学数学科学学院中国天津市300071 中佛罗里达大学理学院美国佛罗里达州

著名的Naimark定理和Stinespring扩张定理表明每一个正算子值测度都有投影值扩张,作用于C^(*)-代数上的每一个完全有界线性映射都可以扩张为有界*-同态,这些都是Hilbert扩张.然而,在交换和非交换情形下,对于任意算子值测度和线性映射,... 详细信息

著名的Naimark定理和Stinespring扩张定理表明每一个正算子值测度都有投影值扩张,作用于C^(*)-代数上的每一个完全有界线性映射都可以扩张为有界*-同态,这些都是Hilbert扩张.然而,在交换和非交换情形下,对于任意算子值测度和线性映射,都有基于Banach空间的一般扩张理论存在.这种一般的扩张理论最终可得到有界线性映射和算子值测度的分类理论.该文简要介绍含幺元代数和向量空间上代数版本的线性系统扩张理论,通过引进典则扩张和万有扩张两种自然的扩张结构,给出所有的线性极小同态扩张的主要分类结果;从Stinespring扩张出发,介绍C^(*)-代数上完全有界线性映射的刻画并说明即使对交换的纯原子的von Neumann代数也存在没有Hilbert扩张的例子.

关键词：线性系统万有扩张完全有界映射 C^(*)-代数