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| 1 | Operator valued frames and structured quantum channels显示文摘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. | HAN DeGuang LI PengTong MENG Bin TANG WaiShing | 2011 | Science China Mathematics2011，54，11： | 8 |
| 2 | Derivations and Isomorphisms of Certain Reflexive Operator Algebras | 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 | 1998 | Acta Mathematica Sinica,English Series1998，14，1： | 3 |
| 3 | Constructing super Gabor frames:the rational time-frequency lattice case显示文摘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. | 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 | 2010 | Science China Mathematics2010，53，12： | 3 |
| 4 | CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES显示文摘This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that erevy linear derivation of a nest algebra algN is continuous provided that one of the following conditions is satisfied:(1)0+(包含)0.(2)X-(包含于)X.(3)there exists a non-trivial idempotnet p in algN such that the range of p belongs to N, It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite dimemnsional. | HAN DEGUANG Department of Mathematics, Qufa Normal University, Qufu 273165, Shandong, China. | 1996 | Chinese Annals of Mathematics,Series B1996，17，2： | 3 |
| 5 | Sampling expansios for functions having values in a Banach space显示文摘 | Han Deguang Zayed A I | 2005 | Proc Amer Math Soc2005，133，12： | 1 |
| 6 | When a Characteristic Function Generates a Gabor Frame 显示文摘 | Gu Qing Han Deguang | 2008 | Appl Comput Harmon Anal2008，24，3： | 1 |
| 7 | Spectrum of the prod- ucts of operators and compact perturbations显示文摘 | Gong Weibang Han Deguang | 1994 | Pro- ceedings of the American Mathematical Society1994，120，： | 1 |
| 8 | Larson,bases and group representations显示文摘 | Deguang Han D R | | 0，，697： | 1 |
| 9 | Frames,bases and gro up repres entatpons显示文摘 | David R Larson | 2000 | Memoirs AMS2000，，： | 1 |
| 10 | Structural Properties of Homomorphism Dilation Systems显示文摘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 spaces.By 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. | Deguang HAN David R.LARSON Bei LIU Rui LIU | 2020 | Chinese Annals of Mathematics,Series B2020，41，4： | 1 |
| 11 | Optimal dual frames for erasures显示文摘 | Jerry Lopez Deguang Han | 2009 | Linear Algebra and Its Applications2009，，1： | 1 |
| 12 | Subspace Weyl-Heisenberg frames显示文摘 | Jean-Pierre Gabardo Deguang Han | 2001 | The Journal of Fourier Analysis and Applications2001，，4： | 1 |
| 13 | Super-wavelets and decomposable wavelet frames显示文摘 | GU Qing HAN Deguang | 2005 | The Journal of Fourier Analysis and Applications2005，11，6： | 1 |
| 14 | Spectrum of the products of operators and compact perturbations 显示文摘 | Gong Weibang Han Deguang | 1994 | Proceedings of the American Mathematical Society1994，120，： | 1 |
| 15 | On the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames显示文摘 | Deguang Han David R. Larson | 2009 | Acta Applicandae Mathematicae (-)2009，，1： | 1 |
| 16 | Dilations and Completions for Gabor Systems显示文摘 | Deguang Han | 2009 | Journal of Fourier Analysis and Applications2009，，2： | 1 |
| 17 | Balian-Low phenomenon for subspace Gabor frames 显示文摘 | Gabardo J P Han Deguang | 2004 | Journal of Mathematical Physics2004，45，8： | 1 |
| 18 | On multiresolution analysis wavelets in Rn显示文摘 | Han Deguang | 2000 | J Fourier Anal Appl2000，6，4： | 1 |
| 19 | Balian-Low phenomenon for subspaee gabor frames 显示文摘 | GABARDO J P HAN Deguang | 2004 | Journal of Mathematical Physics2004，45，8： | 1 |
| 20 | Frames Associated with Measurable Spaces显示文摘 | Jean-Pierre Gabardo Deguang Han | 2003 | Advances in Computational Mathematics (-)2003，，2： | 1 |
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