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RIESZ FRAMES AND APPROXIMATION OF THE FRAME COEFFICIENTS 被引量:3
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作者 Peter G.Casazza Ole Christensen 《Analysis in Theory and Applications》 1998年第2期1-11,共11页
A frame is a fmaily {f_i}_(i=1)~∞ of elements in a Hilbert space with the property that every element in can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can cho... A frame is a fmaily {f_i}_(i=1)~∞ of elements in a Hilbert space with the property that every element in can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coef- ficients. From the mathematical point of view this is gratifying, but for applications it is a problem that the calculation requires inversion of an operator on The projection method is introduced in order to avoid this problem. The basic idea is to con- sider finite subfamilies {f_i}_(i=1)~n of the frame and the orthogonal projection P_n onto its span. For f∈P_n f has a representation as a linear combination of f_i,i=1,2,…,n and the correspond- ing coefficients, can be calculated using finite dimensional methods. We find conditions implying that those coefficients converge to the correct frame coefficients as n→∞, in which case we have avoided the inversion problem. In the same spirit we approximate the solution to a moment prob- lem. It turns out, that the class of 'well-behaving frames' are identical for the two problems we consider. 展开更多
关键词 riesz frames AND APPROXIMATION OF THE FRAME COEFFICIENTS
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Fusion-Riesz frame in Hilbert space
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作者 LI Xue-bin YANG Shou-zhi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第3期339-352,共14页
Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some impo... Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame. 展开更多
关键词 fusion-riesz frame riesz frame of subspace riesz frame exact fusion frame
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Asymmetric Multi-channel Sampling in a Series of Shift Invariant Spaces
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作者 Adam Zakria 《Journal of Mathematics and System Science》 2016年第9期352-365,共14页
We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v(φ(ta)) with a series of Riesz generators ∑a^m=1φ(ta) in L2(R), where each channeled signal is assigned a uniform bu... We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v(φ(ta)) with a series of Riesz generators ∑a^m=1φ(ta) in L2(R), where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v(φ(ta))and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v(φ(ta)). 展开更多
关键词 Shift invariant space Multi-channel sampling Frame riesz basis
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