Continuous $ k $-Frames and their Dual in Hilbert Spaces

Author(s):

Gholamreza Rahimlou , Reza Ahmadi * , MohammadAli Jafarizadeh , Susan Nami

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a c$k$-frame and prove some new results about it.

Keywords:

c-frame , $K$-frame , c$K$-frame , c$k$-atom , c$k$-dual

Language:
English
Published:
Sahand Communications in Mathematical Analysis, Volume:17 Issue: 3, Summer 2020
Pages:
145 to 160
https://www.magiran.com/p2155281  
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