Document Type : Research Paper


1 Department of Mathematics, Shabestar Branch,Islamic Azad University, Shabestar, Iran.

2 Institute of Fundamental Science, University of Tabriz, Tabriz, Iran.

3 Faculty of Physic, University of Tabriz, Tabriz, Iran.


The notion of $k$-frames was recently introduced by G\u avru\c 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.


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