连续g-框架的刻画

肖祥春, 曾晓明

数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1131-1144.

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数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1131-1144. DOI: 10.12386/A2012sxxb0109
论文

连续g-框架的刻画

    肖祥春1, 曾晓明2
作者信息 +

Characterizations of Continuous g-Frames

    Xiang Chun XIAO1, Xiao Ming ZENG2
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文章历史 +

摘要

用合成算子和两个连续g-Bessel序列的有界线性算子L去刻画连续g-框架和连续g-Riesz基; 也从一个给定连续g-框架去构造新的连续g-框架,证明了在合适的条件下在一个给定连续g-框架的基础上去掉某些元素后剩余的部分还能构成连续g-框架.

Abstract

We characterize the continuous g-frames and the continuous g-Riesz basis by the synthesis operator and a bounded operator L associated with two continuous g-Bessel sequences; we also construct new continuous g-frames from a given continuous g-frame. Finally we show that, under some proper conditions, the remainder of some given continuous g-frame by deleting some elements can also be a continuous g-frame.

关键词

连续g-框架 / 连续g-Riesz基 / 可测 / 冗余

Key words

continuous g-frame / continuous g-Riesz basis / measurable / excess

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肖祥春, 曾晓明. 连续g-框架的刻画. 数学学报, 2012, 55(6): 1131-1144 https://doi.org/10.12386/A2012sxxb0109
Xiang Chun XIAO, Xiao Ming ZENG. Characterizations of Continuous g-Frames. Acta Mathematica Sinica, Chinese Series, 2012, 55(6): 1131-1144 https://doi.org/10.12386/A2012sxxb0109

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基金

国家自然科学基金资助项目(61170324);福建省自然科学基金资助项目(2012J01005);福州大学科研启动项目(022410)及福州大学科技发展基金项目(2012-XQ-29)
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