References
Arendt, W., Prüss, J.: Vector-valued Tauberian theorems and asymptotic behavior of linear Volterra equations. SIAM J. Math. Anal.23, 412–448 (1992)
Berg, C., Forst, G.: Potential Theory on Locally Compact Abelian Groups. Berlin Heidelberg New York: Springer 1975
Bingham, N.H.: Fluctuation theory in continuous time. Adv. Appl. Prob.7, 705–766 (1975)
Carasso, A.S., Kato, T.: On subordinated holomorphic semigroups. Trans. Am. Math. Soc.327, 867–878 (1991)
Clément, Ph., Nohel, J.A.: Abstract linear and nonlinear Volterra equations preserving positivity. SIAM. J. Math. Anal.10, 365–388 (1979)
Clément, Ph., Nohel, J.A.: Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels. SIAM. J. Math. Anal.12, 514–535 (1981)
Clément, Ph., Da Prato, G.: Some results on nonlinear heat equations for materials of fading memory type. J. Integral Equations Appl.2, 375–391 (1990)
Clément, Ph., Prüss, J.: Completely positive measures and Feller semigroups. Math. Ann.287, 73–105 (1990)
Da Prato, G., Iannelli, M.: Existence and regularity for a class of integrodifferential equations of parabolic type. J. Math. Anal. Appl.112, 36–55 (1985)
Feller, W.: An introduction to probability theory and its applications. (II) 2nd. ed. New York: Wiley 1971
Fujita, Y.: A probabilistic approach to Volterra equations in Banach spaces. Differential Integral Equations5, 769–776 (1992)
Fujita, Y.: A sufficient condition for the Carasso-Kato theorem. Math. Ann.297, 335–341 (1993)
Grimmer, R.C., Kappel, F.: Series expansions for resolvents of Volterra integrodifferential equations in Banach space. SIAM J. Math. Anal.15, 595–604 (1984)
Grimmer, R.C., Pritchard, A.J.: Analytic resolvent operators for integral equations in Banach space. J. Differ. Equations50, 234–259 (1983)
Gripenberg, G.: Volterra integro-differential equations with accretive nonlinearity. J. Differ. Equations60, 57–79 (1985)
Gripenberg, G., Londen, S.O., Staffans, O.: Volterra Integral and Functional Equations. Cambridge: Cambridge University Press 1990
Kato, T.: Note on fractional powers of linear operators. Proc. Japan Acad.36, 94–96 (1960)
Kolsrud, T.: On a class of probabilistic integrodifferential equations. In: Ideas and methods in mathematical analysis, stochastics, and applications, (S. Albeverio, J.E. Fenstad, H. Holden and T. Lindstrom eds.,) Cambridge University Press, Cambridge (1991)
Lunardi, A.: Laplace transform methods in integrodifferential equations. J. Integral Equations10, 185–211 (1985)
Lunardi, A.: On the linear heat equation with fading memory. SIAM. J. Math. Anal.21, 1213–1224 (1990)
Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Berlin Heidelberg New York: Springer 1983
Yosida, K.: Fractional powers of infinitesimal generators and the analyticity of the semigroups generated by them. Proc. Japan Acad.36, 86–89 (1960)
Yosida, K.: Functional analysis. 6th. ed. Berlin Heidelberg New York: Springer 1980
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Fujita, Y. Holomorphic resolvent for integrodifferential equation with completely positive measure. Math. Ann. 300, 29–40 (1994). https://doi.org/10.1007/BF01450474
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DOI: https://doi.org/10.1007/BF01450474