Results 161 to 170 of about 21,050 (203)

Riesz Basis Property for Generic Network of Strings

2007 Chinese Control Conference, 2006
In this paper, we study the generation problem of Riesz basis for a generic network of strings with joint damping at all vertices. First we give spectral basic property of system operator A. Under certain conditions we prove that the spectrum of A distributes in a strip parallel to the imaginary axis.
Guo Yanni, Xu Genqi, Yang Lingling
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Riesz basis, Paley-Wiener class and tempered splines

Science in China Series A: Mathematics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fang, Gensun, Long, Jingfan
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Riesz Basis Generation: Dual-Basis Approach

2019
This chapter is devoted to the Riesz basis property for wave-like equations. It follows the routs from concrete example to abstract framework. This demonstrates the overall technique. In this chapter, the adjoint basis approach in various situations is introduced, which makes use of the Riesz basis property of exponential families, in particular, the ...
Bao-Zhu Guo, Jun-Min Wang
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Riesz Basis Generation: Comparison Method

2019
This chapter provides a panoramic view on the comparison method. It discusses systematically how the comparison method is used to derive the Riesz basis generation for systems described by partial differential equations. A basic assumption for comparison method to be working is that the feedback can be considered as a perturbation of the system itself,
Bao-Zhu Guo, Jun-Min Wang
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Riesz basis of exponential family for a hyperbolic system

Journal of Applied Analysis, 2019
Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper.
Intissar, Abdelkader, Jeribi, Aref, Walha, Ines   +2 more
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Riesz Basis Generation: Green Function Approach

2019
In this chapter, we discuss another approach for Riesz basis the so-called Green function approach. This happens for beam equations where the boundary feedback control is of the same order as the original but we cannot apply the approach in Chapter 4 for this situation because the exponential family is usually not Riesz basis for the spectrum not being
Bao-Zhu Guo, Jun-Min Wang
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Riesz basis of wavelets constructed from trigonometric B-splines

Analysis and Applications, 2015
In this paper, we construct a class of compactly supported wavelets by taking trigonometric B-splines as the scaling function. The duals of these wavelets are also constructed. With the help of these duals, we show that the collection of dilations and translations of such a wavelet forms a Riesz basis of 𝕃2(ℝ).
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Riesz Basis Property and Stability of Planar Networks of Controlled Strings

Acta Applicandae Mathematicae, 2009
The paper studies the basis property of root vectors of star-shaped networks of strings whose exterior ends are clamped and common node has a damping. The main operator determined by the network is non-normal. By the asymptotic technique, it is shown that its spectrum is in a strip parallel to the imaginary axis, and there is a sequence of root vectors
Han, Zhong Jie, Wang, Lei
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Stability and Riesz basis property for general network of strings

Journal of Dynamical and Control Systems, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Yan Ni, Xu, Gen Qi
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The Riesz Basis Property with Brackets for Dirac Systems with Summable Potentials

Journal of Mathematical Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savchuk, A. M., Sadovnichaya, I. V.
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