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 paper we consider a systematic study of several new Lp-boundedness properties for the index 2F1-transform over spaces L?,p (R+), 1 ? p < ?, R, and L? (R+). We also obtain Parseval-type relations these spaces.

ABSTRACT In modern electronic circuits pose a reliability threat, a many applications are necessary to use protection against soft errors, there is no exceptions in the field of communications and signal processing systems. In new trend interesting option is to use Algorithmic Based Fault Tolerant techniques (ABFT) that try to develop the algorithmic properties to detect and correct the errors....