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Publication . Article . Preprint . 2020

Sobolev functions on closed subsets of the real line

Pavel Shvartsman;
Open Access
Published: 01 Feb 2020 Journal: Journal of Approximation Theory, volume 250, page 105,327 (issn: 0021-9045, Copyright policy )
Publisher: Elsevier BV
Abstract

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

Subjects by Vocabulary

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

Subjects

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

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

[6] C. K. Chui and P. W. Smith, On Hm,∞-splines, SIAM J. Numer. Anal. 11 (1974) 554-558.

[7] C. K. Chui, P. W. Smith, and J. D. Ward, Favard's solution is the limit of Wk,p-splines, Trans. Amer. Math. Soc. 220 (1976) 299-305.

[8] C. K. Chui, P. W. Smith, and J. D. Ward, Quasi-Uniqueness in L∞ Extremal Problems, J. Approx. Theory 18, (1976) 213-219.

[9] C. de Boor, A remark concerning perfect splines, Bull. Amer. Math. Soc. 80 (1974) 724-727. [OpenAIRE]

[10] C. de Boor, On ”best” interpolation, J. Approx. Theory 16 (1976) 28-42.

[14] C. de Boor, Splines as linear combinations of B-splines. A survey, Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976), pp. 1-47. Academic Press, New York, 1976.

[30] M. Golomb, Hm,p-extensions by Hm,p-splines, J. Approx. Theory 5 (1972) 238-275. [OpenAIRE]

[31] A. Israel, A Bounded Linear Extension Operator for L2,p(R2), Annals of Math. 178 (2013) 1-48.

[32] A. Jakimovski, D. C. Russell, On an interpolation problem and spline functions. General inequalities, 2 (Proc. Second Internat. Conf., Oberwolfach, 1978), pp. 205-231, Birkhuser, Basel-Boston, Mass., 1980.

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