Logarithmic convexity results for holomorphic semigroups

Keith Miller

Vol. 58 (1975), No. 2, 549–551

DOI: 10.2140/pjm.1975.58.549

Abstract

The classical logarithmic convexity inequality, for solutions of u′ = −Au with A a self adjoint operator on Hilbert space, yield that u is small at intermediate times, 0 < t ≦ T, provided that u is small at T and bounded at 0. Use of the Carleman inequality for analytic functions allows one to easily generalize this result to the case of operators A which are generators of holomorphic semigroups on Ranach space.

Mathematical Subject Classification

Primary: 47D05

Milestones

Received: 25 July 1974

Published: 1 June 1975