Abstract
This section is devoted to the theory of analytic resolvents, the analog of analytic semigroups for Volterra equations of scalar type. A complete characterization of such resolvents in terms of Laplace transforms is given. In contrast to the general generation theorem of Section 1, the main result of this section, Theorem 2.1, requires conditions which are much simpler to check; this is done in several illustrating examples. The spatial regularity of analytic resolvents is studied and a characterization of analytic semigroups in these terms is derived. It is shown that analytic resolvents lead to improved perturbation results and stronger properties of the variation of parameter formulas.
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© 1993 Springer Basel
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Prüss, J. (1993). Analytic Resolvents. In: Evolutionary Integral Equations and Applications. Modern Birkhäuser Classics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0499-8_2
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DOI: https://doi.org/10.1007/978-3-0348-0499-8_2
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0498-1
Online ISBN: 978-3-0348-0499-8
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