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Concerning the domains
of generators of linear semigroups
J. W. Spellmann |
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Vol. 35 (1970), No. 2, 503–509
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Abstract |
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Let S denote a Banach space over the real numbers. Let A denote the infinitesimal generator of a strongly continuous semigroup T of bounded linear transformations on S. It is known that the Riemann integral ∫ abT(x)pdx is in the domain of A (denoted by D(A)) for each p in S and each nonnegative number interval [a,b]. This paper develops sufficient conditions on nonnegative continuous functions f and on elements p in S in order that the Riemann integral ∫ abT(f(x))pdx be an element of the domain of A. |
Mathematical Subject Classification
Primary: 47.50
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Milestones
Received: 26 February 1970
Published: 1 November 1970
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Authors |
| J. W. Spellmann | |
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