Name
Abstract | ||
|---|---|---|
Let X be a compact, connected, Riemannian manifold (without boundary), @r be the geodesic distance on X, @m be a probability measure on X, and {@f"k} be an orthonormal (with respect to @m) system of continuous functions, @f"0(x)=1 for all x@?X, {@?"k}"k"="0^~ be a nondecreasing sequence of real numbers with @?"0=1, @?"k@6~ as k-~, @P"L:=span{@f"j:@?"j@?L}, L=0. We describe conditions to ensure an equivalence between the L^p norms of elements of @P"L with their suitably discretized versions. We also give intrinsic criteria to determine if any system of weights and nodes allows such inequalities. The results are stated in a very general form, applicable for example, when the discretization of the integrals is based on weighted averages of the elements of @P"L on geodesic balls rather than point evaluations. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jco.2011.03.002 | J. Complexity |
Keywords | DocType | Volume |
Quadrature formulas,Marcinkiewicz–Zygmund inequalities,Riemannian manifold,intrinsic criterion,geodesic distance,general form,Marcinkiewicz-Zygmund measure,probability measure,Data defined manifolds,point evaluation,Discretization inequalities,continuous function,geodesic ball,p norm,nondecreasing sequence | Journal | 27 |
Issue | ISSN | Citations |
6 | Journal of Complexity | 9 |
PageRank | References | Authors |
0.66 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| F. Filbir | 1 | 23 | 3.52 |
| Hrushikesh Narhar Mhaskar | 2 | 257 | 61.07 |