On the Weyl-Heisenberg frames generated by simple functions
Publication in refereed journal

香港中文大學研究人員

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替代計量分析
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其它資訊
摘要Let phi(x) = Sigma(infinity)(n=0) c(n)chi(E)(x - n) with {c(n)}(n=0)(infinity) is an element of l(1), and let (phi,a, 1), 0 < a <= 1 be a Weyl-Heisenberg system {e(2 pi imx) phi(x - na): m, n is an element of Z}. We show that if E = [0, 1] (and some modulo extension of E), then (phi, a, 1) is a frame for each 0 < a <= 1 (for certain a, respectively) if and only if the analytic function H(z) = Sigma(infinity)(n=0) c(n)z(n) has no zero on the unit circle {z: vertical bar z vertical bar = 1}. These results extend the case of Casazza and Kalton (2002) [6] that phi(x) = Sigma(k)(i=1) chi([0, 1])(x - n(i)) and a = 1, which brought together the frame theory and the function theory on the closed unit disk. Our techniques of proofs are based on the Zak transform and the distribution of fractional parts of {na}(n is an element of Z). (c) 2011 Elsevier Inc. All rights reserved.
著者He XG, Lau KS
期刊名稱Journal of Functional Analysis
出版年份2011
月份8
日期15
卷號261
期次4
出版社Elsevier
頁次1010 - 1027
國際標準期刊號0022-1236
電子國際標準期刊號1096-0783
語言英式英語
關鍵詞Analytic function; Fractional part; Frame; Modulation; Translation; Zak transform; Zero
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2021-26-02 於 00:12