References
Arendt, W.,Vector-valued Laplace transforms and Cauchy problems, Israel J. Math.59 (1987), 327–352.
Ball, J. M.,Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Math. Soc.63 (1977), 370–373.
Da Prato, G. and E. Sinestrari,Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa14 (1987), 285–344.
deLaubenfelds R.,Integrated semigroups, C-semigroups and the abstract Cauchy problem, Semigroup Forum41 (1990), 83–95.
deLaubenfels, R., “Existence families, functional calculi and evolution equations,” Springer Verlag Lecture Notes in Math. 1570, 1994.
Desch, W. and W. Schappacher,Some generation results for perturbed semigroups, in “Semigroup Theory and Applications,” Proceedings of Conference, Trieste 1987, Ph. Clement, S. Invernizzi, E. Mitidieri, I. Vrabie (eds.), Lecture Notes in Pure and Applied Math.116, Marcel-Dekker (1989), 125–152.
Desch, W., W. Schappacher and K. Zhang,Semilinear evolution equations, Houston J. Math.15 (1989), 527–552.
Diekmann, O., M. Gyllenberg and H. Thieme,Perturbing semigroups by solving Stieltjes renewal equations, Diff. and Int. Eqns.6 (1993), 155–181.
Goldstein, J. A., “Semigroups of Operators and Applications,” Oxford, New York, 1985.
Grimmer, R. and J. H. Liu,Integrated semigroups and integrodifferential equations, Semigroup Forum48 (1994), 79–95.
Kellermann, H. and M. Hieber,Integrated semigroups, J. Func. Anal.84 (1989), 160–180.
Nagel, R. and E. Sinestrari,Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators. In: K. D. Bierstedt, A. Pietsch, W. M. Ruess, D. Vogt (eds.): Functional Analysis, Proc. Essen Conference, Lect. Notes Pure Appl. Math.150, Marcel-Dekker (1974), 51–70.
Nagel, R. and E. Sinestrari,Nonlinear hyperbolic Volterra integrodifferential equations, preprint, 1995.
Pazy, A., “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer, New York, 1983.
Piskarev, S. and S. Shaw,Multiplicative perturbations of C 0-semigroups and some applications to step responses and cumulative outputs, J. Func. Anal.128 (1995), 315–340.
Travis, C. C.,Differentiability of weak solutions to an abstract inhomogeneous differential equations, Proc. Amer. Math. Soc.82 (1981), 425–430.
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Communicated by J. A. Goldstein
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DeLaubenfels, R., Yao, F. Regularized semigroups of bounded semivariation. Semigroup Forum 53, 369–383 (1996). https://doi.org/10.1007/BF02574151
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DOI: https://doi.org/10.1007/BF02574151