Related papers: Multiresolution analysis on compact Riemannian man…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
The objective of this article is to describe a construction of Parseval bandlimited and localized frames on sub-Riemannian compact homogeneous manifolds.
Our article is a summary of some results for Riemannian manifolds that were obtained in \cite{gpes}-\cite{Pesssubm}. To the best of our knowledge these are the pioneering papers which contain the most general results about frames, Shannon…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…
This paper gives a survey of methods for the construction of space-frequency concentrated frames on Riemannian manifolds with bounded curvature, and the applications of these frames to the analysis of function spaces. In this general…
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large…
In this letter we exhibit the relation between the isometries of a Riemannian contraction of a sub-Riemannian manifold and those of the sub-Riemannian metric, for to use this relation with two goals: establishing a result about the…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
This is an overview article. In his Habilitationsvortrag, Riemann described infinite dimensional manifolds parameterizing functions and shapes of solids. This is taken as an excuse to describe convenient calculus in infinite dimensions…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
We show that one can characterize the Besov spaces on a smooth compact oriented Riemannian manifold, for the full range of indices, through a knowledge of the size of frame coefficients, using the frames we have constructed in [8].
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…