SHIFT-INVARIANT BI-INNER PRODUCT FUNCTIONALS ARE INNER PRODUCTS  

作　　者：Charles K. Chui (1)   Xianliang Shi (1) 

机构地区：[1]1. Department of Mathematics, Texas A & M University, 77843-3368, College Station, TX, USA

出　　处：《Analysis in Theory and Applications》1999年第1期103-110,共8页分析理论与应用（英文刊）

摘　　要：Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.

关 键 词：oscillatory integral operator MULTIPLIER SINGULARITY 

分 类 号：O174.41[理学—数学]