Results 171 to 180 of about 1,296 (214)
Riesz basis for strongly continuous groups [PDF]
Journal of Differential Equations, 2010 17 ...
Hans Zwart
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The expansion of a semigroup and a Riesz basis criterion
Journal of Differential Equations, 2005 Let \(\mathcal{A}\) be the generator for a strongly continuous semigroup \(T(t)\) on a Hilbert space \(X\). Suppose that the singular set for \(\mathcal{A}\) can be split into two parts \(\sigma(\mathcal{A})=\sigma_1(\mathcal{A})\cup\sigma_2(\mathcal{A})\), where \(\sigma_2(\mathcal{A})\) consists all isolated eigenvalues. Under the assumption that the
Genqi Xu
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Riesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass
SIAM Journal on Control and Optimization, 2001Summary: Using an abstract condition of Riesz basis generation of discrete operators in the Hilbert spaces, we show, in this paper, that a sequence of generalized eigenfunctions of an Euler-Bernoulli beam equation with a tip mass under boundary linear feedback control forms a Riesz basis for the state Hilbert space.
Bao-Zhu Guo
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Angle criteria for frame sequences and frames containing a Riesz basis
Journal of Mathematical Analysis and Applications, 2008 We obtain a condition implying that the union of two frame sequences is also a frame sequence. Christensen found a condition for this in terms of orthogonal projections. We phrase our condition by use of the angle between closed subspaces.
Ha, Young-Hwa +2 more
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Integral Equations and Operator Theory, 2013 We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points.
Branko Ćurgus +2 more
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Riesz Basis Generation: Dual-Basis Approach
2019This 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 of exponential family for a hyperbolic system
Journal of Applied Analysis, 2019Abstract 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 +2 more
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Riesz Basis Property for Generic Network of Strings
2007 Chinese Control Conference, 2006In 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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The Riesz Basis Property with Brackets for Dirac Systems with Summable Potentials
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savchuk, A. M., Sadovnichaya, I. V.
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Riesz Basis Generation: Comparison Method
2019This 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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