Name
Title | ||
|---|---|---|
Extension of sampling inequalities to Sobolev semi-norms of fractional order and derivative data |
Abstract | ||
|---|---|---|
This paper, devoted to sampling inequalities, provides some extensions of previous results by Arcangéli et al. (Numer Math 107(2):181–211, 2007; J Approx Theory 161:198–212, 2009). Given a function u in a suitable Sobolev space defined on a domain Ω in $${{\mathbb{R}}^n}$$, sampling inequalities typically yield bounds of integer order Sobolev semi-norms of u in terms of a higher order Sobolev semi-norm of u, the fill distance d between $${\overline\Omega}$$ and a discrete set $${A\subset\overline\Omega}$$, and the values of u on A. The extensions established in this paper allow us to bound fractional order semi-norms and to incorporate, if available, values of partial derivatives on the discrete set. Both the cases of a bounded domain Ω and $${\Omega={\mathbb{R}}^n}$$ are considered. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00211-011-0439-3 | Numerische Mathematik |
Keywords | Field | DocType |
higher order sobolev semi-norm,suitable sobolev space,numer math,discrete set,bounded domain,derivative data,sampling inequality,j approx theory,function u,bound fractional order semi-norms,integer order sobolev semi-norms | Integer,Discrete mathematics,Mathematical optimization,Approx,Mathematical analysis,Sobolev space,Partial derivative,Omega,Sampling (statistics),Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
121 | 3 | 0945-3245 |
Citations | PageRank | References |
5 | 0.47 | 9 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rémi Arcangéli | 1 | 29 | 2.74 |
| María Cruz López de Silanes | 2 | 35 | 3.37 |
| Juan José Torrens | 3 | 36 | 4.06 |
| López de SilanesMaría Cruz | 4 | 10 | 0.96 |
| TorrensJuan José | 5 | 10 | 0.96 |