PRECISE BEHAVIOUR OF THE APPROXIMATION NUMBERS OF THE SOBOLEV EMBEDDING IN THE ONE-DIMENSION CASE

JAN LANG

langjan@yahoo.com, lang@math.ohio-state.edu

Department of Mathematics
The Ohio State University
231 W 18th Avenue
Columbus, OH 43210, USA

N We consider the Sobolev embedding and . We show that for all in the -th approximation number of is given by

where is a constant dependent only on . We also find the best dimensional linear approximation of and we will discuss the shape of unit ball in .

EPSRC Gregynog Workshop, 21-26 July 2002