Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization...

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.

The theme is to smooth characteristic functions of Parseval frame wavelet sets by convolution in order to obtain implementable, computationally viable, smooth wavelet frames. We introduce the following: a new method to improve frame bound estimation; a shrinking technique to construct frames; and a nascent theory concerning frame bound gaps. The phenomenon of a frame bound gap occurs when certa...

We establish several results yielding linear independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding linear independence is that the space V (ψ) is shift-invariant. In particular, the affine system generated by a Parseval wavelet is linearly independent. As an illustration of our techniques, we give an alt...

Here we list the equal norm Parseval frames for Hilbert spaces as of 2005. We will continue to update this list as new examples become known. The first author was supported by NSF DMS 0405376. 1

The paper introduced the task designing ideas, data preparation methods, evaluation metrics and results of the second Chinese syntactic parsing evaluation (CIPS-Bakeoff-ParsEval-2010) jointed with SIGHAN Bakeoff tasks.

In this paper, we study the finite Hankel transformation on spaces of generalized functions by developing a new procedure. We consider two Hankel type integral transformations hμ and h∗μ connected by the Parseval equation

In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.