WIENER’S LEMMA FOR INFINITE MATRICES
WIENER’S LEMMA FOR INFINITE MATRICES
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DOI：
10.1090/s0002-9947-07-04303-6
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发表时间：
2006
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影响因子：
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通讯作者：
Qiyu Sun
中科院分区：
文献类型：
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作者：
Qiyu Sun
经典的维纳引理及其各种推广是重要的，并在数值分析，小波理论，框架理论和采样理论中有许多应用。经典Wiener引理有许多不同的等价形式，其中一个等价形式适合于我们的推广，涉及无限矩阵的交换代数W：= {（a（j − j））j，j′∈Zd：∑ j∈Zd| a（j）|< ∞}。在样条逼近、（扩散）小波与仿射框架、非均匀网格上的Gabor框架、非均匀采样与重构等问题的研究中，无穷矩阵的伴随代数都是极端非交换的，但我们期望这些非交换代数具有与交换代数W的Wiener引理相似的性质。本文考虑了两个无限矩阵的非交换代数Schur类和Sjöstrand类，建立了这两类矩阵代数的Wiener引理.
The classical Wiener lemma and its various generalizations are important and have numerous applications in numerical analysis, wavelet theory, frame theory, and sampling theory. There are many different equivalent formulations for the classical Wiener lemma, with an equivalent formulation suitable for our generalization involving commutative algebra of infinite matrices W := {(a(j − j))j,j′∈Zd : ∑ j∈Zd |a(j)| < ∞}. In the study of spline approximation, (diffusion) wavelets and affine frames, Gabor frames on non-uniform grid, and non-uniform sampling and reconstruction, the associated algebras of infinite matrices are extremely non-commutative, but we expect those noncommutative algebras to have a similar property to Wiener’s lemma for the commutative algebra W. In this paper, we consider two non-commutative algebras of infinite matrices, the Schur class and the Sjöstrand class, and establish Wiener’s lemmas for those matrix algebras.