A New Identity for Parseval Frames
نویسندگان
چکیده
In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.
منابع مشابه
A Fundamental Identity for Parseval Frames
Frames are an essential tool for many emerging applications such as data transmission. Their main advantage is the fact that frames can be designed to be redundant while still providing reconstruction formulas. This makes them robust against noise and losses while allowing freedom in design (see, for example, [5, 10]). Due to their numerical stability, tight frames and Parseval frames are of in...
متن کاملProperties of J-fusion Frames in Krein Spaces
In this article we introduce the notion of J-Parseval fusion frames in a Krein space K and characterize 1-uniform J-Parseval fusion frames with ζ = √ 2. We provide some results regarding construction of new J-tight fusion frame from given J-tight fusion frames. We also characterize an uniformly J-definite subspace of a Krein space K in terms of J-fusion frame. Finally we generalize the fundamen...
متن کاملSimple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm
In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...
متن کاملFurther Results on the Connectivity of Parseval Frame Wavelets
New ideas were introduced in [3] to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.
متن کاملOptimal properties of the canonical tight probabilistic frame
A probabilistic frame is a Borel probability measure with finite second moment whose support spans R. A Parseval probabilistic frame is one for which the associated matrix of second moment is the identity matrix in R. Each probabilistic frame is canonically associated to a Parseval probabilistic frame. In this paper, we show that this canonical Parseval probabilistic frame is the closest Parsev...
متن کامل