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# Sobolev functions on closed subsets of the real line

For each $p>1$ and each positive integer $m$ we use divided differences to give intrinsic characterizations of the restriction of the Sobolev space $W^m_p(R)$ to an arbitrary closed subset of the real line.

41 pages

Microsoft Academic Graph classification: Sobolev space Discrete mathematics Mathematics Divided differences Real line Integer

Applied Mathematics, General Mathematics, Numerical Analysis, Analysis, Mathematics - Functional Analysis, 46E35, Functional Analysis (math.FA), FOS: Mathematics

Applied Mathematics, General Mathematics, Numerical Analysis, Analysis, Mathematics - Functional Analysis, 46E35, Functional Analysis (math.FA), FOS: Mathematics

Microsoft Academic Graph classification: Sobolev space Discrete mathematics Mathematics Divided differences Real line Integer

###### 21 references, page 1 of 3

sup{k f |S kLm∞(R)|S : S ⊂ E, #S = m + 1} = sup m! |Δm f [xi, ..., xi+m]| . i

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For each $p>1$ and each positive integer $m$ we use divided differences to give intrinsic characterizations of the restriction of the Sobolev space $W^m_p(R)$ to an arbitrary closed subset of the real line.

41 pages