Vol. 35, No. 2, 1970

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Concerning the domains of generators of linear semigroups

J. W. Spellmann

Vol. 35 (1970), No. 2, 503–509

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
Received: 26 February 1970
Published: 1 November 1970
J. W. Spellmann