Open AccessInterpolation and extrapolation of smooth functions by linear operators
Author(s) -
Charles Fefferman
Publication year - 2005
Publication title -
revista matemática iberoamericana
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.569
H-Index - 52
eISSN - 2235-0616
pISSN - 0213-2230
DOI - 10.4171/rmi/424
Subject(s) - extrapolation , interpolation (computer graphics) , linear interpolation , mathematics , linear operators , operator theory , mathematical analysis , computer science , computer graphics (images) , polynomial , bounded function , animation
Let Cm,1(Rn) be the space of functions on Rn whose mth derivatives are Lipschitz 1. For E Rn, let Cm,1(E) be the space of all restrictions to E of functions in Cm,1(Rn). We show that there exists a bounded linear operator T : Cm,1(E) ! Cm,1(Rn) such that, for any f 2 Cm,1(E), we have Tf = f on E.
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