- Projections and Dyadic Parseval Body MRA Wavelets
Authors: Peter M. Luthy, Guido L. Weiss, Edward N. Wilson
Summary: A classical theorem attributed to Naimark states that, given a Parseval body B in a Hilbert house H, one can embed H in a bigger Hilbert house Ok in order that the picture of B is the projection of an orthonormal foundation for Ok. Within the current work, we revisit the notion of Parseval body MRA wavelets from two papers of Paluszyński, Šikić, Weiss, and Xiao (PSWX) and produce an analog of Naimark’s theorem for these wavelets on the degree of their scaling capabilities. We intention to make this dialogue as self-contained as potential and supply a special standpoint on Parseval body MRA wavelets than that of PSWX.
2. Shannon Sampling and Parseval Frames on Compact Manifolds
Authors: Isaac Z. Pesenson
Summary: Our article is a abstract of some outcomes for Riemannian manifolds that had been obtained in cite{gpes}-cite{Pesssubm}. To the perfect of our data these are the pioneering papers which include probably the most basic outcomes about frames, Shannon sampling, and cubature formulation on compact and non-compact Riemannian manifolds. Specifically, the paper cite{gpes} offers an “finish level” building of tight localized frames on homogeneous compact manifolds. The paper cite{Pessubm} is the primary systematic growth of localized frames on compact domains in Euclidean areas.
