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Polynomial Trace Estimates for Semigroups

Authors:	Blunck S.

Affiliation:	(1) Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany (e-mail

Abstract:	For semigroups (e^tA)_t0 of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type $parallel {kern 1pt} {text{e}}^{tA} {kern 1pt} parallel _{;{mathfrak{G}}_1 } leqslant Ct^{ - alpha } ,t >0$ , where ${mathfrak{G}}_1$ denotes the trace class. As an application we present higher order analogues of results due to E.B. Davies, B. Simon and M. van den Berg of the type $parallel {kern 1pt} {text{e}}^{tDelta _Omega } {kern 1pt} parallel _{;{mathfrak{G}}_1 } leqslant Ct^{ - alpha } ,t >0$ , for certain unbounded domains $Omega subset mathbb{R}^n$ , e.g. spiny urchin domains.

Keywords:	semigroups of operators trace estimates higher order operators approximation numbers Sobolev imbeddings
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