We construct Parseval wavelet frames in $$L^2(M)$$ for a general Riemannian manifold M and we show the existence of unconditional $$L^p(M)$$ $$1< p <\infty $$ . This is made possible thanks to smooth orthogonal projection decomposition identity operator on , which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). also characterization Triebel–Lizorkin $${\mathbf {F}}_{p,q}^s...

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.

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.