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GROWTH ESTIMATES FOR SINE-TYPE-FUNCTIONS AND APPLICATIONS TO RIESZ BASES OF EXPONENTIALS
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作者 Alexander M. Lindner (Technische Universitat Munchen, Germany) 《Approximation Theory and Its Applications》 2002年第3期26-41,共16页
We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive expl... We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem, of Bogmtr, Horvath, Job and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riese bases is desirable. 展开更多
关键词 GROWTH ESTIMATES FOR SINE-TYPE-FUNCTIONS AND APPLICATIONS TO riesz bases OF EXPONENTIALS
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INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS 被引量:1
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作者 臧丽丽 孙文昌 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1939-1944,共6页
In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is ... In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory. 展开更多
关键词 FRAMES g-frames riesz bases g-riesz bases
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THE RECOVERY OF FUNCTIONS OF PALEY-WIENER CLASS FROM IRREGULAR SAMPLINGS
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作者 房艮孙 陈雪冬 《Acta Mathematica Scientia》 SCIE CSCD 2002年第4期466-472,共7页
It is shown that a function f which is in the classical Paley-Wiener class, and its k-th derivative f((k)) can be recovered in the metric L-q (R), 2 < q < infinity, from its values on irregularly distributed dis... It is shown that a function f which is in the classical Paley-Wiener class, and its k-th derivative f((k)) can be recovered in the metric L-q (R), 2 < q < infinity, from its values on irregularly distributed discrete sampling set {t(j)}(j)is an element ofz as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {t(j)}(jis an element ofz) is a real sequence such that {e(j)(it)(zeta)} j(is an element ofz) constitutes a Riesz basis for L-2([-pi, pi]). 展开更多
关键词 tempered spline interpolation Paley-Wienerclass riesz bases
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Riesz multiwavelet bases generated by vector refinement equation 被引量:3
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作者 LI Song LIU ZhiSong 《Science China Mathematics》 SCIE 2009年第3期468-480,共13页
In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ ... In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L 2(? s ). Suppose ψ = (ψ1,..., ψ r ) T and $ \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T $ are two compactly supported vectors of functions in the Sobolev space (H μ(? s )) r for some μ > 0. We provide a characterization for the sequences {ψ jk l : l = 1,...,r, j ε ?, k ε ? s } and $ \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s $ to form two Riesz sequences for L 2(? s ), where ψ jk l = m j/2ψ l (M j ·?k) and $ \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-0em} 2}} \tilde \psi ^\ell (M^j \cdot - k) $ , M is an s × s integer matrix such that lim n→∞ M ?n = 0 and m = |detM|. Furthermore, let ? = (?1,...,? r ) T and $ \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T $ be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, $ \tilde a $ and M, where a and $ \tilde a $ are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr ) T and $ \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T $ , ν = 1,..., m ? 1 such that two sequences {ψ jk νl : ν = 1,..., m ? 1, l = 1,...,r, j ε ?, k ε ? s } and { $ \tilde \psi _{jk}^\nu $ : ν=1,...,m?1,?=1,...,r, j ∈ ?, k ∈ ? s } form two Riesz multiwavelet bases for L 2(? s ). The bracket product [f, g] of two vectors of functions f, g in (L 2(? s )) r is an indispensable tool for our characterization. 展开更多
关键词 vector refinement equations riesz multiwavelet base biorthogonal wavelets 42C40 39B12 46B15 47A10 47B37
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Density Results for Subspace Multiwindow Gabor Systems in the Rational Case
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作者 Qiao Fang LIAN Hai Li MA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第5期897-912,共16页
Let S be a periodic set in R and L2(S) be a subspace of L2(R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time- frequency shift parameters... Let S be a periodic set in R and L2(S) be a subspace of L2(R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time- frequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in L2(S). Under such conditions, we construct a multiwindow tight Gabor frame for L2 (S) with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for L2(S), and obtain the density condition for a multiwindow Gabor Riesz basis for L2 (S). 展开更多
关键词 Multiwindow Gabor frames riesz bases SUBSPACES Zak transform density conditions
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A Note on Shift-Invariant Spaces Admitting a Single Generator
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作者 Jun Jian ZHAO1,21.Department of Mathematics,Tianjin Polytechnic University,Tianjin 300160,P.R.China 2.College of Applied Sciences,Beijing University of Technology,Beijing 100124,P.R.China 《Journal of Mathematical Research and Exposition》 CSCD 2011年第1期123-128,共6页
In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2(0, 1) and L^2(R). In this paper, in terms of bases for L^... In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2(0, 1) and L^2(R). In this paper, in terms of bases for L^2(0, α), two sampling theorems for αZ-shift invariant spaces with a single generator are obtained. 展开更多
关键词 shift-invariant spaces sampling riesz bases.
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