Vol. 107, No. 1, 1983

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Extensions of d∕dx that generate uniformly bounded semigroups

Ralph Jay De Laubenfels

Vol. 107 (1983), No. 1, 95–105
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
Authors
Ralph Jay De Laubenfels