%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 ck-frame %K ck-atom %K ck-dual %R 10.22130/scma.2019.115719.691 %X The notion of $k$-frames was recently introduced by G\u avru\c 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 https://scma.maragheh.ac.ir/article_40583_dc1f525dd6b30726e40f65c66c109e27.pdf