WAVELET BASES FOR A UNITARY OPERATOR

被引:8
作者
LEE, SL [1 ]
TAN, HH [1 ]
TANG, WS [1 ]
机构
[1] NATL UNIV SINGAPORE,DEPT MATH,SINGAPORE 0511,SINGAPORE
关键词
D O I
10.1017/S0013091500019064
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let T be a unitary operator on a complex Hilbert space H and X, Y be finite subsets of H We give a necessary and sufficient condition for T-Z(X):={T(n)x:n is an element of Z, x is an element of X} to be a Riesz basis of its closed linear span [T(Z)X]>. If T-Z(X) and T-Z(Y) are Riesz bases, and [T-Z(X)]subset of[T-Z(Y)], then X is extendable to X' such that T-Z(X') is a Riesz basis of [T-Z(Y)]. The proof provides an algorithm for the construction of Riesz bases for the orthogonal complement of [T-Z(X)] in [T-Z(Y)]. In the case X consists of a single B-spline, the algorithm gives a natural and quick construction of the spline wavelets of Chui and Wang [2, 3]. Further, the duality principle of Chui and Wang in [3] and [4] is put in the general setting of biorthogonal Riesz bases in Hilbert space.
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收藏
页码:233 / 260
页数:28
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