%0 Journal Article
%T Continuous $ k $-Frames and their Dual in Hilbert Spaces
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Rahimlou, Gholamreza
%A Ahmadi, Reza
%A Jafarizadeh, Mohammad Ali
%A Nami, Susan
%D 2020
%\ 07/01/2020
%V 17
%N 3
%P 145-160
%! Continuous $ k $-Frames and their Dual in Hilbert Spaces
%K c-frame
%K $K$-frame
%K c$K$-frame
%K c$k$-atom
%K c$k$-dual
%R 10.22130/scma.2019.115719.691
%X The notion of $k$-frames was recently introduced by Gu avruc ta in HilbertĀ 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.
%U http://scma.maragheh.ac.ir/article_40583_8baad0d22b5a702687eb584294dd9657.pdf