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C*-Algebra BH(I) Consisting of Bessel Sequences in a Hilbert Space

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Journal of Mathematical Research with Applications 2015年第2期35卷 191-199页

作者： Zhihua GUO Maoren YIN Huaixin CAO College of Mathematics and Information Science Shaanxi Normal University Department of Mathematics Junior College of Xinzhou Teachers University

Let H be a separable Hilbert space, B H(I), B(H) and K(H) the sets of all Bessel sequences {f i}i∈I in H, bounded linear operators on H and compact operators on H, respectively. Two kinds of multiplications and involutions are introduced in light of two isometric linear isomorphisms αH : B H(I) → B(?2), β : B H(I) → B(H), respectively, so that B H(I) becomes a unital C*-algebra under each kind of multiplication and involution. It is proved that the two C*-algebras(B H(I), ?, ?) and(B H(I), ·, *) are *-isomorphic. It is also proved that the set F H(I) of all frames for H is a unital multiplicative semi-group and the set R H(I) of all riesz bases for H is a self-adjoint multiplicative group, as well as the set K H(I) := β-1(K(H)) is the unique proper closed self-adjoint ideal of the C*-algebra B H(I).

关键词： C *-algebra Bessel sequence Hilbert space frame riesz basis

riesz bases of multivariate translates for Sobolev space

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商丘师范学院学报 2010年第9期26卷 7-12页

作者： ZHANG Guobing DING Xuanhao JIANG Yingchun School of Mathematics and Computational Science Guilin University of Electronic TechnologyGuilin 541004China

This paper gives a systematic study of riesz bases of multivariate translates derived from a fixed compactly supported multivariate function in a Sobolev *** with a multivariate function φ satisfying a very mild condition in Sovolev space Hs(Rd),we provide a necessary and sufficient condition under which {φ(x-n)}n∈Zd is a riesz basis for span{φ(x-n)}n∈Zd.

关键词： Sobolev space riesz basis generalized bracket product biorthogonalty

NON-ORTHOGONAL P-WAVELET PACKETS ON THE HALF-LINE

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Analysis in Theory and Applications 2012年第4期28卷 385-396页

作者： F.A. Shah University of Kashmir

In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.

关键词： p-Multiresolution analysis p-wavelet packets riesz basis Walsh function,Walsh-Fourier transform

The Relations between Discrete Frames and Continuous Frames with Respect to （N, μ）

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Chinese Quarterly Journal of Mathematics 2013年第4期28卷 503-509页

作者： LIU Chun-tai School of Mathematics and Computer Science Wuhan Polytechnic University Wuhan 430023 China

The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.

关键词： frame continuous frame measurable space riesz basis excess

Stability Analysis of Cooperation System of Two Robot Arms

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Stability Analysis of Cooperation System of Two Robot Arms

Dynamic boundary stabilization of Euler-Bernoulli beam through a Kelvin-Voigt damped wave equation

第二十九届中国控制会议

作者： CHEN Yunlan1,2,XU Genqi1 1.Department of Mathematics,Tianjin University,Tianjin 300072,P.R.China2.Department of Automation,Tianjin University,Tianjin 300072,P.R.China

In this paper we study the stability problem of a hybrid system composed of two robots,where the appropriate cooperation of robots are expected to work *** performance of system depends directly upon one main factor:the coordination movement of the *** stability analysis of the system results in a model of uniform Euler-Bernoulli beams with linear and non-collocated boundary feedback *** prove that the system is exponentially stable with suitable choice of parameters of the *** particular,we show that the system satisfies the spectrum determine growth condition.

关键词： Robot Arms cooperative System Euler-Bernoulli Beam Non-collocated Control riesz basis Exponential Stabil-ity

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Dynamic boundary stabilization of Euler-Bernoulli beam throu...

Stability of a Controlled Strings Network With a Circuit

第26届中国控制与决策会议

作者： Lu Lu Jun-Min Wang School of Mathematics Beijing Institute of Technology

In this paper, we study the stability of a one-dimentional Euler-Bernoulli beam coupled with a KelvinVoigt damped wave equation, where the wave equation acts as a dynamic boundary feedback controller to exponentially stabilize the Euler-Bernoulli beam. Remarkably, the resolvent of the closed-loop system operator is not compact *** a detailed spectral analysis, we show that the residual spectrum is empty and the continuous spectrum contains only one point. Moreover, we verify that the generalized eigenfunctions of the system forms a riesz basis for the energy state space. It then follows that the C0-semigroup generated by the system operator satisfies the spectrum-determined growth assumption. Finally, the exponential stability and Gevrey regularity of the system are established.

关键词： Euler-Bernoulli equation Kelvin-Voigt damping spectrum asymptotic analysis riesz basis stability.

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Stability of a Controlled Strings Network With a Circuit

CHARACTEIZATIONS OF WOVENT g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACESS AND C^(*)-MODULES

2010 Chinese Control and Decision Conference

作者： Dongyi Liu~(1,2),Genqi Xu~(3,4) 1.School of Science,Tianjin University,Tianjin,300072,P R China 2.School of Electrical Engineering and Automation,Tianjin University,Tianjin 300072,China 3.School of Science,Tianjin University,Tianjin,300072,P R China 4.School of Electrical Engineering and Automation,Tianjin University,Tianjin 300072,China

A strings network with a circuit is considered under the assumptions that the network is connected and are fixed at the exterior nodes and that the controllers are placed on the inner nodes of the *** the semigroup theory and the spectral analysis,it is shown that the system satisfies the riesz basis property and the spectrum determined growth ***,by the spectral analysis in imaginary axis,some sufficient conditions are provided for the asymptotical stability of the network.

关键词： Elastic strings network Spectral analysis riesz basis Spectrum determined growth condition Asymptotical stability Closed loop system

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Acta Mathematica Scientia 2023年第6期43卷 2471-2482页

作者： Amir KHOSRAVI Mohammad Reza FARMANI Faculty of Mathematical Sciences and Computer Kharazmi University599 Taleghani Ave.Tehran 15618Iran

In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-***,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal ***,we have a note about a comment and a relation in the proof of Proposition 5.3 in[*** et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-riesz bases,woven and P-woven g-frames.

关键词： g-frame fusion frame woven frame riesz basis g-riesz basis