【摘要】 文章通过有界可逆算子,引入了Hilbert空间中控制连续框架概念,并给出控制连续框架的一些基本性质.控制连续框架是控制框架和连续框架的推广,它具有很多类似于连续框架的性质.另外,文章应用算子论的方法,讨论了控制连续框架的扰动性,且表明连续框架或Bessel集在一定条件下为控制连续框架,控制连续框架在一定条件下为连续框架.更多还原

【Abstract】 In this paper, the concept of controlled continuous frame in Hilbert spaces is introduced by bounded inverse operator, and some basic properties of controlled continuous frame are given. The controlled continuous frame is the promotion of controlled frame and continuous frame, which has many properties similar to continuous frame.In addition, we discuss the perturbation of controlled continuous frames by using operator theory, and show that continuous frame or Bessel set is a controlled continuous frame under certain conditions, and controlled continuous frame is continuous frame under certain conditions.更多还原