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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Preasymptotic estimates for approximation of multi
variate periodic Sobolev functions - Thomas Kuehn
(Universität Leipzig )
DTSTART;TZID=Europe/London:20190221T090000
DTEND;TZID=Europe/London:20190221T093500
UID:TALK120187AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/120187
DESCRIPTION:Approximation of Sobolev functions is a topic with
a long history and many applications in different
branches of mathematics. The asymptotic order as
$n\\to\\infty$ of the approximation numbers $a_n$
is well-known for embeddings of isotropic Sobolev
spaces and also for Sobolev spaces of dominating m
ixed smoothness. However\, if the dimension $d$ of
the underlying domain is very high\, one has to w
ait exponentially long until the asymptotic rate b
ecomes visible. Hence\, for computational issues t
his rate is useless\, what really matters is the p
reasymptotic range\, say $n\\le 2^d$. \;

In the talk I will first give a short overview ove
r this relatively new field. Then I will present s
ome new preasymptotic estimates for $L_2$-approxim
ation of periodic Sobolev functions\, which improv
e the previously known results. I will discuss the
cases of isotropic and dominating mixed smoothnes
s\, and also $C^\\infty$-functions of Gevrey type.
Clearly\, on all these spaces there are many equi
valent norms. It is an interesting effect that - i
n contrast to the asymptotic rates - the preasympt
otic behaviour strongly depends on the chosen norm
.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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