摘要
广义正交基是Hilbert空间中正交基的一个自然推广.本文首先给出一个广义正交基存在的较弱的充要条件;然后研究广义正交基的性质,特别地,得到广义正交基版本的一些有关正交基的经典性质,如广义正交基的Bessel等式和不等式等.作为广义正交基的一个应用,本文给出广义Riesz基的一些新刻画.最后本文讨论广义框架的冗余问题.
g-Orthonormal basis is a natural generalization of orthonormal basis in Hilbert spaces. In this paper, firstly, we give a general condition such that the g-orthonormal bases exist. Then we consider the properties of g-orthonormal basis. In particular, we establish the g-orthonormal basis versions of some classical properties of orthonormal basis, such as Bessel inequality and Bessel equality etc. We also give some new characterizations of g-Riesz bases. Finally, we discuss the redundancy problem of g-frames.
出处
《中国科学：数学》
CSCD
北大核心
2013年第10期1047-1058,共12页
Scientia Sinica：Mathematica
