Vol. 58, No. 2, 1975

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Logarithmic convexity results for holomorphic semigroups

Keith Miller

Vol. 58 (1975), No. 2, 549–551
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
Authors
Keith Miller