This is a preview of subscription content, log in via an institution to check access.
References
Abramowitz, M., Stegun, I.: Handbook of mathemtical functions. New York: Dover 1970
Adams, R.A.: Sobolev spaces (Pure and Appl. Math., vol. 65) New York: Academic Press 1975
Borchers, W., Sohr, H.: On the semigroup of the Stokes operator in exterior domains. Math. Z.196, 415–425 (1987)
Burkholder, D.L.: Martingales and Fourier analysis in Banach spaces. In: Letta, G., Pratelli, M. (eds.) Probability and analysis. (Lect. Notes Math., vol. 1206, pp. 61–108) Berlin Heidelberg New York: Springer 1986
Clement, P., Prüss, J.: Completely positive kernels and Feller semigroups. Preprint (1989) in preparation
Dore, G., Venni, A.: On the closedness of the sum of two closed operators. Math. Z.196, 189–201 (1987)
Dore, G., Venni, A.: Some results on complex powers of closed operators. Preprint (1988)
Giga, Y.: Domains of fractional powers of the Stokes operator inL r -spaces. Arch. Rat. Mech. Anal.89, 251–265 (1985)
Giga, Y., Sohr, H.: On the Stokes operator in exterior domains. J. Fac. Sc. Tokyo Univ., Sec. IA,36, 103–130 (1989)
Giga, Y., Sohr, H.: Note on the Cauchy problem in Banach spaces with applications to the Navier-Stokes equation in exterior domains. Preprint (1988)
Hille, E., Phillips, R.S.: Semigroups and functional analysis. Providence, RI: Am. Math. Soc. Colloq. Publ. 31 (1957)
Komatsu, H.: Fractional powers of operators. Pac. J. Math.1, 285–346 (1966)
Krein, S.G.: Linear differential equations in Banach spaces. Providence, RI: Transl. Math. Monographs 29, Am. Math. Soc. (1972)
Pipkin, A.C.: Lectures on viscoelasticity theory. (Appl. Math. Sciences, vol. 7) Berlin Heidelberg New York: Springer 1972
Prüss, J.: Positivity and regularity of hyperbolic Volterra equations in Banach spaces. Math. Anal.19, 317–344 (1987)
Prüss, J.: Regularity and integrability of resolvents of linear Volterra equations in Banach spaces. Proceedings of the Conference ‘Volterra Integrodifferential Equations in Banach Spaces’, Trento 1987, London: Longman (to appear in 1989)
Prüss, J.: Linear hyperbolic Volterra equations of scalar type. Proceedings of the Conference ‘Trends in Semigroup Theory and Applications’, Trieste 1987. Lect. Notes Pure Appl. Math.116, 367–384 (1989)
Seeley, R.: Norms and domains of the complex powerA Z B . Am. J. Math.93, 299–309 (1971)
Stein, E.: Topics in harmonic analysis. Princeton: Princeton University Press 1970
Sz-Nagy, B., Foias, C.: Harmonic analysis of operators on Hilbert space. Amsterdam: North Holland 1970
Titchmarsh, E.C.: Introduction to the theory of Fourier integrals, 2nd edn. Oxford: Clarendon Press 1948
Widder, D.V.: The Laplace transform. Princeton: Princeton University Press 1941
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prüss, J., Sohr, H. On operators with bounded imaginary powers in banach spaces. Math Z 203, 429–452 (1990). https://doi.org/10.1007/BF02570748
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02570748