Extensions of d∕dx that generate uniformly bounded semigroups

Ralph Jay De Laubenfels

Vol. 107 (1983), No. 1, 95–105

DOI: 10.2140/pjm.1983.107.95

Abstract

A ≡−d∕dx on BC₀(R⁺), 𝒟(A) ≡{f ∈ BC₀(R⁺)∣f′∈ BC₀(R⁺)}, is an example of a maximal accretive operator that does not generate a contraction semigroup. It does, however, have extensions that generate uniformly bounded semigroups. A large class of such extensions are presented. The same is done with d∕dx and −d∕dx on C₀[0,1].

Mathematical Subject Classification 2000

Primary: 47B44

Secondary: 47E05, 47D05

Milestones

Received: 24 September 1981

Published: 1 July 1983