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111.
Andrea Blunck 《Discrete Mathematics》2005,301(1):46-56
The set G of all m-dimensional subspaces of a 2m-dimensional vector space V is endowed with two relations, complementarity and adjacency. We consider bijections from G onto G′, where G′ arises from a 2m′-dimensional vector space V′. If such a bijection ? and its inverse leave one of the relations from above invariant, then also the other. In case m?2 this yields that ? is induced by a semilinear bijection from V or from the dual space of V onto V′.As far as possible, we include also the infinite-dimensional case into our considerations. 相似文献
112.
The finite section method and problems in frame theory 总被引:1,自引:0,他引:1
The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz basis. 相似文献
113.
Somantika Datta 《Linear and Multilinear Algebra》2016,64(8):1484-1497
Lower bounds on the maximal cross correlation between vectors in a set were first given by Welch and then studied by several others. In this work, this is extended to obtaining lower bounds on the maximal cross correlation between subspaces of a given Hilbert space. Two different notions of cross correlation among spaces have been considered. The study of such bounds is done in terms of fusion frames, including generalized fusion frames. In addition, results on the expectation of the cross correlation among random vectors have been obtained. 相似文献
114.
115.
Email: otsuka{at}j.dendai.ac.jp
Received on November 11, 2005; Accepted on December 16, 2006 In this paper, necessary and sufficient conditions for the parameterinsensitive disturbance-rejection problem with dynamic outputfeedback which was studied in Otsuka (1999) to be solvable aregiven for the structured uncertain linear systems. Further,necessary and sufficient conditions for the solvability of theproblems with static output feedback and state feedback arealso studied as special cases. The obtained results containsome extensions of the previous results to the structured uncertainlinear systems. 相似文献
116.
Stefan Ericsson 《Journal of Mathematical Analysis and Applications》2011,373(1):271-286
An important cornerstone of both wavelet and sampling theory is shift-invariant spaces, that is, spaces V spanned by a Riesz basis of integer-translates of a single function. Under some mild differentiability and decay assumptions on the Fourier transform of this function, we show that V also is generated by a function with Fourier transform for some g with . We explain why analysis of this particular generating function can be more likely to provide large jitter bounds ε such that any f∈V can be reconstructed from perturbed integer samples f(k+εk) whenever supk∈Z|εk|?ε. We use this natural deconvolution of to further develop analysis techniques from a previous paper. Then we demonstrate the resulting analysis method on the class of spaces for which g has compact support and bounded variation (including all spaces generated by Meyer wavelet scaling functions), on some particular choices of φ for which we know of no previously published bounds and finally, we use it to improve some previously known bounds for B-spline shift-invariant spaces. 相似文献
117.
Piotr Koszmider Przemys?aw Zieliński 《Journal of Mathematical Analysis and Applications》2011,376(1):329-341
Let Γ denote an uncountable set. We consider the questions if a Banach space X of the form C(K) of a given class (1) has a complemented copy of c0(Γ) or (2) for every c0(Γ)⊆X has a complemented c0(E) for an uncountable E⊆Γ or (3) has a decomposition X=A⊕B where both A and B are nonseparable. The results concern a superclass of the class of nonmetrizable Eberlein compacts, namely Ks such that C(K) is Lindelöf in the weak topology and we restrict our attention to Ks scattered of countable height. We show that the answers to all these questions for these C(K)s depend on additional combinatorial axioms which are independent of ZFC ± CH. If we assume the P-ideal dichotomy, for every c0(Γ)⊆C(K) there is a complemented c0(E) for an uncountable E⊆Γ, which yields the positive answer to the remaining questions. If we assume ♣, then we construct a nonseparable weakly Lindelöf C(K) for K of height ω+1 where every operator is of the form cI+S for c∈R and S with separable range and conclude from this that there are no decompositions as above which yields the negative answer to all the above questions. Since, in the case of a scattered compact K, the weak topology on C(K) and the pointwise convergence topology coincide on bounded sets, and so the Lindelöf properties of these two topologies are equivalent, many results concern also the space Cp(K). 相似文献
118.
S. Jung 《Journal of Mathematical Analysis and Applications》2011,379(1):325-260
In this paper we study properties of complex symmetric operators. In particular, we prove that every complex symmetric operator having property (β) or (δ) is decomposable. Moreover, we show that complex symmetric operator T has Dunford?s property (C) and it satisfies Weyl?s theorem if and only if its adjoint does. 相似文献
119.
120.
Dongfeng ShiChengyu Fan Hong ShenPengfei Zhang Jinghui ZhangChunhong Qiao Yingjian Wang 《Optics Communications》2012,285(24):4937-4940
A new single-frame blind deconvolution algorithm for the linear shift-invariant imaging system is presented. The algorithm processes the partial images segmented from one single degraded image by multi-frame approach to recover the point spread function (PSF). Then a deconvolution method is employed to restore the whole image with the recovered PSF. In addition, in order to improve the fidelity and resolution of the recovered PSF, the coprimeness of the partial images is utilized. Results of simulated and real atmospheric turbulence degraded images using the algorithm are reported. 相似文献