Polynomial trace estimates for semigroups (Q1598520)

This paper is based on the author's Ph.D. Thesis written at Kiel University. His summary is as follows: For semigroups \((e^{tA})_{t\geq 0}\) of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type \(\|e^{tA}\|_{{\mathfrak G}_1}\leq Ct^{-\alpha}\), \(t> 0\), 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 \(\|e^{t\Delta_\Omega}\|_{{\mathfrak G}_1}\leq Ct^{-\alpha}\), \(t> 0\), for certain unbounded domains \(\Omega\subset \mathbb{R}^n\), e.g. spiny urchin domains.