Journal of Operator Theory

Volume 53, Issue 2, Spring 2005 pp. 225-249.

Semigroups growth bounds

Authors: E.B. Davies
Author institution: Department of Mathematics, King's College London,\break Strand, London WC2R 2LS, England

Summary: $\newcommand{\R}{\mathbb{R}}$ We use the Legendre transform to find a relationship between the norms of a one-parameter semigroup and those of its resolvent operators. The theorems are illustrated with a variety of examples, particularly estimates of the norms of the semigroups associated with Schrödinger operators, considered as acting on the space $L^1(\R^n)$.

Keywords: One-parameter semigroups, growth bounds, resolvent norms, Schrödinger operators, spectral theory.

Contents Full-Text PDF