arXiv subjects
Publications and source records attributed to Zahra Darvishi.
In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will be clarified through examples.
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may not be defined. To overcome this problem, the new concept namely Q-dual for c-fusion frames will be defined and some of its properties will be investigated.
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $Ω$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.