Continuous $ k $-Frames and their Dual in Hilbert Spaces
Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 3)Publication Date: 2020-07-01
Authors : Gholamreza Rahimlou; Reza Ahmadi; Mohammad Ali Jafarizadeh; Susan Nami;
Page : 145-160
Keywords : c-frame; $K$-frame; c$K$-frame; c$k$-atom; c$k$-dual;
Abstract
The notion of $k$-frames was recently introduced by Gu avruc 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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