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

Abstract

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.

Keywords

• c-frame
• $k$-frame
• c$k$-frame
• c$k$-atom
• c$k$-dual