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Journal of Systems Science & Complexity 2014年第3期27卷 463-475页

作者： ZHAO Dongxia WANG Junmin Department of Mathematics North University of China School of Mathematics Beijing Institute of Technology

In this paper, an interconnected wave-ODE system with K-V damping in the wave equation and unknown parameters in the ODE is considered. It is found that the spectrum of the system operator is composed of two parts： Point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point 1 1/d, and there are two branches of the asymptotic eigenvalues： The first branch is accumulating towards 1 -2, and the other branch tends to -∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a riesz basis for the Hilbert state space. As a consequence, the spectrum-determined growth condition and exponential stability of the system are concluded.

关键词： Exponential stability Kelvin-Voigt damping riesz basis spectrum wave equation.

A characterization of generator for multiresolution analysis with composite dilations

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Applied Mathematics(A Journal of Chinese Universities) 2014年第3期29卷 317-328页

作者： SHI Xian-liang CHEN Jie College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

In this paper, we will introduce multiresolution analysis with composite dilations and give a characterization of generator for multiresolution analysis with composite dilations.

关键词： MRA generator riesz basis composite dilation characterization.

Generalized Sampling in Shift Invariant Spaces with Frames

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Acta Mathematica Sinica,English Series 2012年第9期28卷 1823-1844页

作者： Stefan ERICSSON Department of Engineering Sciences and Mathematics Lule University of Technology

Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？

关键词： Generalized sampling frames riesz basis reproducing kernel shift invariant spaces

Construction of a class of multivariate compactly supported wavelet bases for L2（Rd）

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Frontiers of Mathematics in China 2012年第1期7卷 177-195页

作者： Fengying ZHOU Yunzhang LI College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In this paper, for a given d x d we investigate the compactly supported expansive matrix M with ｜ det M｜ = 2, M-wavelets for L^2（R^d）. Starting with N a pair of compactly supported refinable functions and satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet p such that {2J/2b（Mj -k）：j E Z, k c gg} forms a riesz basis for L2（Ra）. The （anti-）symmetry of such ~b is studied, and some examples are also provided.

关键词： riesz basis wavelet refinable function

CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C*-MODULES

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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 University

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 46L99 42C15 46H25

Stability analysis for an Euler-Bernoulli beam under local internal control and boundary observation

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控制理论与应用（英文版） 2008年第4期6卷 341-350页

作者： Junmin WANG Baozhu GUO Kunyi YANG Department of Mathematics Beijing Institute of Technology Beijing 100081 China Academy of Mathematics and Systems Science Academia Sinica Beijing 100080 China

An Euler-Bernoulli beam system under the local internal distributed control and boundary point observation is studied. An infinite-dimensional observer for the open-loop system is designed. The closed-loop system that is non- dissipative is obtained by the estimated state feedback. By a detailed spectral analysis, it is shown that there is a set of generalized eigenfunctions, which forms a riesz basis for the state space. Consequently, both the spectrum-determined growth condition and exponential stability are concluded.

关键词： Euler-Bernoulli equation Observer riesz basis Controllability and observability Stability

Boundary feedback stabilization of a Schrdinger equation interconnected with a heat equation

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控制理论与应用（英文版） 2013年第4期11卷 558-562页

作者： Junjun LIU Junmin WANG School of Mathematics Beijing Institute of Technology

In this paper, we study stabilization for a Schoedinger equation, which is interconnected with a heat equation via boundary coupling. A direct boundary feedback control is adopted. By a detailed spectral analysis, it is found that there are two branches of eigenvalues： one is along the negative real axis, and the other is approaching to a vertical line, which is parallel to the imagine axis. Moreover, it is shown that there is a set of generalized eigenfunctions, which forms a riesz basis for the energy state space. Finally, the spectrum-determined growth condition is held and the exponential stability of the system is then concluded.

关键词： Schroedinger equation Heat equation Boundary control Stability riesz basis

Exponential Stability of a Coupled Heat-ODE System 25th

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Exponential Stability of a Coupled Heat-ODE System

PERTURBATION OF WAVELET AND GABOR FRAMES

第25届中国控制与决策会议

作者： Dong-Xia Zhao Jun-Min Wang the Department of Mathematics Beijing Institute of Technology the Department of Mathematics North University of China the Department of Mathematics Beijing Institute of Technology

ISBN: (纸本)9781467355339

This paper addresses the feedback stabilization of an interconnected Heat-ODE system with the Dirichlet interconnection. The "interconnection" between the heat equation and the ODE are bi-directional, in which the Dirichlet boundary observation of the heat equation is fed into the ODE, and the velocity of ODE is flowed into the boundary of the heat equation. The semigroup approach is adopted in investigation. By a detailed analysis, we obtain the asymptotic expressions of eigenvalues and eigenfunctions. It is shown that there is a sequence of generalized eigenfunctions, which forms a riesz basis for the Hilbert state space. This deduces the spectrumdetermined growth condition for the C0-semigroup, and as a consequence, the exponential stability of the system is then followed. Numerical simulations are presented.

关键词： Heat equation Dirichlet interconnection riesz basis Exponential stability

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Analysis in Theory and Applications 2003年第3期19卷 238-254页

作者： Ivana Carrizo Sergio Favier Instituto de Matemática Aplicada San Luis Universidad Nacional de San Luis Instituto de Matemática Aplicada San Luis Universidad Nacional de San Luis Av.Ejército de Los Andes 950.5700 San LuisArgentinaAv.Ejército de Los Andes 950.5700 San LuisArgentina

In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically, we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.

关键词： riesz basis Gabor frame wavelet frame perturbation