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Mathematische Annalen

, Volume 287, Issue 1, pp 73–105 | Cite as

Completely positive measures and Feller semigroups

  • Philippe Clément
  • Jan Prüss
Article

Keywords

Positive Measure Fell Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Akcoglu, M.A., Sucheston, L.: Dilations of positive contractions onL p spaces. Can. Math. Bull.20, 285–292 (1977)Google Scholar
  2. 2.
    Berg, C., Forst, G.: Potential theory of locally compact groups (Ergebn. Math. Grenzgeb., vol. 87). Berlin Heidelberg New York: Springer 1975Google Scholar
  3. 3.
    Bergh, J., Löfström, J.: Interpolation spaces. An introduction (Grundl. Math. Wiss., vol. 223). Berlin Heidelberg New York: Springer 1976Google Scholar
  4. 4.
    Bochner, S.: Harmonic analysis and the theory of probability. Berkeley, Calif.: University of California Press 1955Google Scholar
  5. 5.
    Clément, Ph.: On abstract Volterra equations in Banach spaces with completely positive kernels. Proc. Conf. Infinite-dimensional systems, Retzhof 1983, (Lect. Notes Math., vol. 1076, 32–40) Berlin Heidelberg New York: Springer 1984Google Scholar
  6. 6.
    Clément, Ph., Egberts, P.: On the sum of two maximal monotone operators. Differ. Integral Equations (to appear)Google Scholar
  7. 7.
    Clément, Ph., Mitidieri, E.: Qualitative properties of solutions of Volterra equations in Banach spaces. Isr. J. Math.64, 1–24 (1988)Google Scholar
  8. 8.
    Clément, Ph., Nohel, J.A.: Abstract linear and nonlinear Volterra equations preserving positivity. SIAM J. Math. Anal.10, 365–388 (1979)Google Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Clément, Ph., DaPrato, G.: Existence and regularity results for an integral equation with infinite delay in a Banach space. Integral Equations Oper. Theory11, 480–500 (1988)Google Scholar
  11. 11.
    Coifman, R.R., Weiss, G.: Transference methods in analysis. Conf. Board Math. Sci., Reg. Conf. Series Math. 31. Am. Math. Soc., Providence, Rhode Island, 1977Google Scholar
  12. 12.
    Dore, G., Venni, A.: On the closedness of the sum of two closed opertors. Math. Z.196, 189–201 (1987)Google Scholar
  13. 13.
    Feller, W.: An introduction to probability theory and its applications, vol. II, 2nd edn. New York: Wiley 1970Google Scholar
  14. 14.
    Friedman, A.: On integral equations of Volterra type. J. Anal. Math.11, 381–413 (1963)Google Scholar
  15. 15.
    Gel'fand, I.M., Raikov, D.A., Shilov, G.E.: Commutative normed rings. New York: Chelsea 1964Google Scholar
  16. 16.
    Gripenberg, G.: On Volterra equations of the first kind. Integral Equations Oper. Theory3/4, 473–488 (1980)Google Scholar
  17. 17.
    Gripenberg, G.: Volterra integro-differential equations with accretive nonlinearity. J. Differ. Eq.60, 57–79 (1985)Google Scholar
  18. 18.
    Hille, E., Phillips, R.S.: Functional analysis and semigroups. Am. Math. Soc. Colloq Publ. 31, Providence, Rhode Island 1957Google Scholar
  19. 19.
    Hirsch, F.: Familles resolvantes, generateurs, cogenerateurs. Ann. Inst. Fourier22, 89–210 (1972)Google Scholar
  20. 20.
    Katznelson, Y.: An introduction to harmonic analysis, 2nd Edn. New York: Dover 1976Google Scholar
  21. 21.
    Kingman, J.F.C.: Regenerative phenomena. New York: Wiley 1972Google Scholar
  22. 22.
    Komatsu, H.: Fractional powers of operators. Pac. J. Math.1, 285–346 (1966)Google Scholar
  23. 23.
    Larsen, R.: An introduction to the theory of multipliers. (Grundl. Math. Wiss., vol. 175) Berlin Heidelberg New York: Springer 1971Google Scholar
  24. 24.
    Levin, J.J.: Resolvents and bounds for linear and nonlinear Volterra equations. Trans. Am. Math. Soc.228, 207–222 (1977)Google Scholar
  25. 25.
    Lunardi, A.: On the linear heat equation for materials of fading memory type. SIAM J. Math. Anal. (to appear)Google Scholar
  26. 26.
    McConnell, T.R.: On Fourier multiplier transformations of Banach-valued functions. Trans. Am. Math. Soc.285, 739–757 (1984)Google Scholar
  27. 27.
    Miller, R.K.: On Volterra integral equations with nonnegative integrable resolvents. J. Math. Anal. Appl.22, 319–340 (1968)Google Scholar
  28. 28.
    Nunziato, J.W.: On heat conduction in materials with memory. Quart. Appl. Math.29, 187–204 (1971)Google Scholar
  29. 29.
    Prüss, J.: Positivity and regularity of hyperbolic Volterra equations in Banach spaces. Math. Ann.279, 314–344 (1987)Google Scholar
  30. 30.
    Prüss, J.: Regularity and integrability of resolvents of linear Volterra equations in Banach spaces. Proc. Conf. Volterra integrodifferential equations in Banach spaces. Trento 1987. London: Longman Scientific and Technical 1989 (Pitman Res. Notes Math., vol. 190, pp. 339–367)Google Scholar
  31. 31.
    Prüss, J.: Linear hyperbolic Volterra equations of scalar type. Proc. Conf. Trends in semigroup theory and applications. Trieste 1987. (Lect. Notes Pure Appl. Math., vol. 116, pp. 367–385). New York: Dekker 1989Google Scholar
  32. 32.
    Prüss, J., Sohr, H.: On operators with bounded imaginary powers. Math. Z. (to appear)Google Scholar
  33. 33.
    Reuter, G.E.H.: Über eine Volterrasche Integralgleichung mit total-monotonem Kern. Arch. Math.7, 59–66 (1956)Google Scholar
  34. 34.
    Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton: Princeton University Press 1971Google Scholar
  35. 35.
    Widder, D.V.: The Laplace transform. Princeton: Princeton University Press 1941Google Scholar
  36. 36.
    Yosida, K.: Functional analysis, 3th Edn. (Grundl. Math. Wiss., vol. 123) Berlin Heidelberg New York: Springer 1971Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Philippe Clément
    • 1
  • Jan Prüss
    • 2
  1. 1.Faculteit voor Wiskunde en InformaticaTechnische Universiteit DelftDelftThe Netherlands
  2. 2.Fachbereich 17 Mathematik und InformatikUniversität-GHS PaderbornPaderbornFederal Republic of Germany

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