Estimates for functions in Sobolev spaces defined on unbounded domains

Authors:
Rémi Arcangéli;María Cruz López de Silanes;Juan José Torrens
Affiliations:
Route de Barat, 31160 Arbas, France;Departamento de Matemática Aplicada, C.P.S., Universidad de Zaragoza, María de Luna, 50018 Zaragoza, Spain;Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain
Venue:
Journal of Approximation Theory
Year:
2009

Citing 2
Cited 1

An estimate for multivariate interpolation II

Journal of Approximation Theory
An extension of a bound for functions in Sobolev spaces, with applications to (m, s)-spline interpolation and smoothing

Numerische Mathematik

Sampling and stability

MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces

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Abstract

Given a function u belonging to a suitable Beppo-Levi or Sobolev space and an unbounded domain @W in R^n, we prove several Sobolev-type bounds involving the values of u on an infinite discrete subset A of @W. These results improve the previous ones obtained by Madych and Potter [W.R. Madych, E.H. Potter, An estimate for multivariate interpolation, J. Approx. Theory 43 (1985) 132-139] and Madych [W.R. Madych, An estimate for multivariate interpolation II, J. Approx. Theory 142 (2006) 116-128].