On weaving frames in Hilbert spaces

In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a condition associated with synthesis operators of frames such that the sequence of frames is woven. Finally, for a family of woven frames, we show that they are stable under invertible operators and small perturbations

Splitting of operator for frame inequalities in Hilbert spaces

In this paper, we obtain a new type of inequalities for frames, which are parametrized by a parameter \lambda\in R . By suitable choices of {\lambda}, one obtains the previous results as special cases. Our new proof also makes the underlying mathematical structure that gives rise to these inequalities more transparent than previous approaches: Our proof shows that the main point is the splitting S = S1 + S2 of the positive denite frame operator S into the two positive semidenite operators S1 and S2

A new probabilistic model for optimal frames in erasure's recovery

In this paper we introduce a new probabilistic model for optimizing erasures occurring in data transmission using Parseval frames and a sequence of Bernoulli random variables associated to the channels of the transmission. We establish several results characterizing the optimal Parseval frames for our model. We show also that compared to existing models \cite{holmes2004optimal,casazza2003equal,leng2013probability,li2018frame}, our model gives better performance