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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Semigroups of unbounded linear operators in Banach space

Author: Rhonda Jo Hughes
Journal: Trans. Amer. Math. Soc. 230 (1977), 113-145
MSC: Primary 47D05
MathSciNet review: 0636372
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Abstract: One-parameter families of unbounded linear operators acting in a Banach space X, and satisfying the semigroup and strong continuity properties on a suitable subspace of X, are discussed; the notion of infinitesimal generator is generalized to this unbounded setting, and a Hille-Yosida-type theorem is proved. The theory is illustrated by several examples, which include fractional integrals and derivatives acting in $ {L^p}(0,\infty )$.

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Keywords: Semigroup of bounded operators, closed operator, resolvent, infinitesimal generator, fractional integral, fractional derivative, Riemann-Liouville semigroup, fractional powers of closed operators
Article copyright: © Copyright 1977 American Mathematical Society