Semigroups of unbounded linear operators in Banach space
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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 ${L^p}(0,\infty )$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 230 (1977), 113-145
- MSC: Primary 47D05
- DOI: https://doi.org/10.1090/S0002-9947-1977-0636372-4
- MathSciNet review: 0636372