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 -