TY - JOUR ID - 40583 TI - Continuous $ k $-Frames and their Dual in Hilbert Spaces JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Rahimlou, Gholamreza AU - Ahmadi, Reza AU - Jafarizadeh, Mohammad Ali AU - Nami, Susan AD - Department of Mathematics, Shabestar Branch,Islamic Azad University, Shabestar, Iran. AD - Institute of Fundamental Science, University of Tabriz, Tabriz, Iran. AD - Faculty of Physic, University of Tabriz, Tabriz, Iran. Y1 - 2020 PY - 2020 VL - 17 IS - 3 SP - 145 EP - 160 KW - c-frame KW - k-frame KW - ck-frame KW - ck-atom KW - ck-dual DO - 10.22130/scma.2019.115719.691 N2 - 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. UR - https://scma.maragheh.ac.ir/article_40583.html L1 - https://scma.maragheh.ac.ir/article_40583_dc1f525dd6b30726e40f65c66c109e27.pdf ER -