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A CHARACTERIZATION OF STRONGLY CONTINUOUS GROUPS OF LINEAR OPERATORS ON A HILBERT SPACE
Published online by Cambridge University Press: 01 January 2000
Abstract
It is proved that the infinitesimal generator A of a strongly continuous semigroup of linear operators on a Hilbert space also generates a strongly continuous group if and only if the resolvent of −A, (λ+A)−1, is also a bounded function on some right-hand-side half plane of complex numbers, and converges strongly to zero as the real part of λ tends to infinity. An application to a partial differential equation is given.
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- © The London Mathematical Society 2000
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