河南科技大学学报（自然科学版）2026，Vol.47Issue(2)：96-104,9.DOI:10.15926/j.cnki.issn1672-6871.2026.02.011
Krein空间中对偶框架的稳定性
The Stability of Dual Frames in Krein Space
摘要
Abstract
The theory and methods of Krein space operators have garnered significant attention due to their important applications in mathematics and engineering.In recent years,the concept of frames has been introduced into Krein spaces.As a generalization of frames,dual frames provide multiple representations for signals,thereby offering more choices and flexibility in signal processing.However,the indefiniteness of the inner product in Krein spaces leads to fundamental differences between its frame theory and that of Hilbert spaces,making classical perturbation stability theories not directly applicable.By employing frame operators and the Minkowski inequality,the stability of dual frames in Krein spaces under perturbations from sequences and Bessel sequences is investigated,and corresponding proofs are provided.关键词
Krein空间/框架/对偶框架/扰动Key words
Krein space/frame/dual frame/perturbation分类
数理科学引用本文复制引用
周慧,张建平,康鑫艺..Krein空间中对偶框架的稳定性[J].河南科技大学学报（自然科学版）,2026,47(2):96-104,9.基金项目
国家自然科学基金项目(11961072) （11961072）
陕西省自然科学基础研究计划项目(2020JM-547) （2020JM-547）
延安大学研究生教育创新计划项目(YKY2025035) （YKY2025035）
