共查询到20条相似文献,搜索用时 0 毫秒
2.
Hans Zwart 《Journal of Differential Equations》2010,249(10):2397-2408
Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (counted with multiplicity) can be grouped into subsets of at most K elements, and the distance between the groups is (uniformly) bounded away from zero, then the spectral projections associated to the groups form a Riesz family. This implies that if in every range of the spectral projection we construct an orthonormal basis, then the union of these bases is a Riesz basis in the Hilbert space. 相似文献
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Based on (J. Approx. Theory 86 (1996) 240), we prove that the integer shifts of a multivariate blockwise polynomial φ(x) which is compactly supported and m-refinable form a Riesz basis if and only if . Here , c≠0 is a constant, B(x|v1,v2,…,vk) is a multivariate box spline and the matrix (v1,v2,…,vk) is unimodular. 相似文献
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Young-Hwa Ha 《Journal of Mathematical Analysis and Applications》2008,347(1):90-95
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. Also a lower bound formula is obtained. We then apply the results to find conditions for a frame containing a Riesz basis to be a Riesz frame. 相似文献
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R. A. Zalik 《Applied and Computational Harmonic Analysis》1999,7(3):315
Recently we found a family of nearly orthonormal affine Riesz bases of compact support and arbitrary degrees of smoothness, obtained by perturbing the one-dimensional Haar mother wavelet using B-splines. The mother wavelets thus obtained are symmetric and given in closed form, features which are generally lacking in the orthogonal case. We also showed that for an important subfamily the wavelet coefficients can be calculated in O(n) steps, just as for orthogonal wavelets. It was conjectured by Aldroubi, and independently by the author, that these bases cannot be obtained by a multiresolution analysis. Here we prove this conjecture. The work is divided into four sections. The first section is introductory. The main feature of the second is simple necessary and sufficient conditions for an affine Riesz basis to be generated by a multiresolution analysis, valid for a large class of mother wavelets. In the third section we apply the results of the second section to several examples. In the last section we show that our bases cannot be obtained by a multiresolution analysis. 相似文献
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SHEN Yi & LI Song 《中国科学 数学(英文版)》2011,(6)
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples.In this paper,we shall construct Riesz wavelet associated with dual pseudo splines.Furthermore,we use dual pseudo splines to construct tight frame systems with desired approximation order by applying the unitary extension principle. 相似文献
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In this paper, we study the Riesz basis property and the problem of stabilization of two vibrating strings connected by a point mass with variable physical coefficients under a boundary feedback control acts at one extreme point and Dirichlet boundary condition on the other end. It is shown that the system has a sequence of generalized eigenfunctions which forms a Riesz basis for the state Hilbert space. By a detailed spectral analysis, it is proved that this hybrid system is asymptotically stable but not exponentially stable. 相似文献
8.
Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. Suppose that A is the generator of a C0 semigroup on a Hilbert space and σ(A)=σ1(A)∪σ2(A) with σ2(A) is consisted of isolated eigenvalues distributed in a vertical strip. It is proved that if σ2(A) is separated and for each λ∈σ2(A), the dimension of its root subspace is uniformly bounded, then the generalized eigenvectors associated with σ2(A) form an L-basis. Under different conditions on the Riesz projection, the expansion of a semigroup is studied. In particular, a simple criterion for the generalized eigenvectors forming a Riesz basis is given. As an application, a heat exchanger problem with boundary feedback is investigated. It is proved that the heat exchanger system is a Riesz system in a suitable state Hilbert space. 相似文献
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J. Levesley 《Numerical Algorithms》1995,10(2):401-419
Quasi-interpolation using radial basis functions has become a popular method for constructing approximations to continuous functions in many space dimensions. In this paper we discuss a procedure for generating kernels for quasi-interpolation, using functions which have series expansions involving terms liker
logr. It is shown that such functions are suitable if and only if is a positive even integer and the spatial dimension is also even. 相似文献
10.
设G是局部紧Abel群,Ω■G是Haar可测集,L~2(Ω)是Ω上Haar平方可积函数构成的Hilbert空间,PWΩ(G):={f∈L~2(G):supp f(ξ)■Ω}是G上的Paley-Wiener空间.本文研究Paley-Wiener空间PWΩ(G)上平移Riesz基和Riesz谱集Ω之间的关系. 相似文献
11.
Sylvain Durand 《Applied and Computational Harmonic Analysis》2019,46(1):122-153
This article addresses the issue of designing bases for that are generated by translations, rotations and dilations of a single mother wavelet ψ. We show how this construction can be simplified by setting an odd number of directions and by choosing properly the phase of the Fourier transform of ψ. A large part of the article is devoted to the proof of theorems that give sufficient conditions for ψ to generate a Riesz sequence and a Riesz basis for . An example of Riesz sequence whose restriction to each scale is orthonormal is set. Theoretical results are confirmed by numerical experiments where a discrete directional wavelet transform is introduced. 相似文献
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Olgun Cabri 《Mathematical Methods in the Applied Sciences》2019,42(18):6733-6740
In this paper, we consider the nonself‐adjoint discontinuous Sturm Liouville operator with periodic (antiperiodic) boundary condition and compatibility conditions. Asymptotic formulas of eigenvalues and eigenfunctions of the operator are obtained. Using these accurate asymptotic formulas for eigenvalues and eigenfunctions, we prove the basisness of the root functions of the boundary value problem. 相似文献
15.
The Riesz basis property of a Timoshenko beam with boundary feedback and application 总被引:3,自引:0,他引:3
The Riesz basis property of the generalized eigenvector systemof a Timoshenko beam with boundary feedback is studied. Firstly,two auxiliary operators are introduced, and the Riesz basisproperty of their eigenvector systems is proved. This propertyis used to show that the generalized eigenvector system of aTimoshenko beam with some linear boundary feedback forms a Rieszbasis in the corresponding state space. Finally, it is concludedthat the closed loop system exhibits exponential stability. 相似文献
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Xu Gen-Qi; Feng De-Xing; Yung Siu Pang 《IMA Journal of Mathematical Control and Information》2004,21(1):65-83
The Riesz basis property of the generalized eigenvector system
of a Timoshenko beam with boundary feedback controls appliedto two ends is studied in this paper. The spectral property
of the operator A determined by the closed loop system is investigated.It is shown that operator A has compact resolvent and generatesa C<sub>0</sub> semigroup, and its spectrum consistsof two branches and has two asymptotes under some conditions.Furthermore it is proved that the sequence of all generalizedeigenvectors of the system principal operator forms a Rieszbasis for the state Hilbert space. 相似文献
19.
研究了具有扭转耦合效应的复合薄壁梁黎斯基的性质以及指数稳定性.首先证明该系统决定算子的预解式是紧的,且可生成群.其次,通过对该系统算子谱的渐近分析,证明了除至多有限个本征值外,其算子的谱是单重可分离的.特殊地,我们获得了自由系统的频率渐近表达式,因而利用克尔德什定理,证明了在希尔伯特状态空间中算子广义本征函数列的完备性.最后,结合黎斯基的性质及算子谱的分布证明了该系统的指数稳定性. 相似文献
20.
We study damped EulerBernoulli beams that have nonuniformthickness or density. These nonuniformfeatures result in variablecoefficient beam equations. We prove that despite the nonuniformfeatures, the eigenfunctions of the beam form a Riesz basisand asymptotic behaviour of the beam system can be deduced withoutany restrictions on the sign of the damping. We also providean answer to the frequently asked question on damping: howmuch more positive than negative should the damping be withoutdisrupting the exponential stability?, and result ina criterion condition which ensures that the system is exponentiallystable. 相似文献