vahid sadri

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we can define analysis, synthesis and frame operators with representation space compatible for (C,C')-Controlled g-fusion frames, which even yield a reconstruction formula. Also, some useful concepts such as Q-dual and perturbation are introduced and investigated.

Regarding the applications of the fusion frames and generalization of them in data proceeding, their iterative is of particular importance when one of their members is deleted. In this note, a method for reconstruction of continuous generalized  usion frames and the error operator with its upper bound are presented. Also, the approximation operator for these frames will be introduced.

In this paper, we will introduce and study “Continuous weaving K-frames in Hilbert spaces”.We first introduce a useful result for the production of these frames and then examine them under the influence of a boundary operator.Due to the basic and useful use of different types of frames in restoring some deleted information in data transfer issues, we have dedicated the end of the paper to the conditions of setting the frame under the removal of some members of the measure space and we will see that, this is related to the discrete K-frames.

In this paper, we intend to introduce the concept of weaving continuous g-frames in separable Hilbert spaces. Then, we present some new results on these frames and also we show that it is enough to check continuous g-woven in smaller measurable space than the original space. We investigate the relationship between these frames and c-woven frames. Sufficient conditions will also be given for these frames. Finally, we verify the perturbation of weaving continuous g-frames.

The study of the ck-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the continuous frames. After improving and extending the concept of fusion frames and continuous frames, in this paper we introduce continuous k-fusion frames in Hilbert spaces. Similarly to the c-fusion frames, dual of continuous k-fusion frames may not be defined, we however define the Q-dual of continuous k-fusion frames. Also some new results and the perturbation of continuous k-fusion frames will be presented.The formula is not displayed correctly!

According to the application of fusion and g-fusion frames in data processing, iterative reconstruction of the frame is of particular importance when a member of the frame is removed. In this paper, we present a way of reconstruction of g-fusion frames and introduce the error operator and we get the upper bound for it. Also, the approximation operator for these frames will be introduced and we study some results about them.