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Interpolation of semigroups and integrated semigroups

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References

  • [Arl] Arendt, W.,Vector valued Laplace transform and Cauchy problems, Israel J. Math.59 (1987), 327–352.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ar2] Arendt, W.,Resolvent positive operators, Proc. London Math. Soc.54 (1987), 321–349.

    Article  MATH  MathSciNet  Google Scholar 

  • [A-K] Arendt, W., and H. Kellermann,Integrated solutions of Volterra integrodifferential equations and applications, In: Integro-differential Equations, Proc. Conf. Trento 1987. G. Da Prato, M. Iannelli (eds.). Pitman. Research Notes in Mathematics190 (1989), 21–51.

  • [Be] Beals, R.,On the abstract Cauchy problem, J. Funct. Anal.10 (1972), 281–299.

    Article  MATH  MathSciNet  Google Scholar 

  • [dL] de Laubenfels, R.,Integrated semigroups, C-semigroups and the abstract Cauchy problem, Semigroup Forum41 (1990), 83–95.

    Article  MathSciNet  Google Scholar 

  • [Do] Doetsch, G.,Handbuch der Laplace-Transformation I, Birkhäuser Verlag, Basel 1950.

    MATH  Google Scholar 

  • [Ka] Kantorovitz, S.,The Hille-Yosida space of an arbitrary operator, J. Math. Anal. Appl.136 (1988), 107–111.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ke] Kellermann, H.,Integrated semigroups, Dissertation, Universität Tübingen, 1986.

  • [K-H] Kellermann, H., and M. Hieber,Integrated semigroups, J. Functional Anal.84 (1989), 160–180.

    Article  MathSciNet  Google Scholar 

  • [K-L-C] Krein, S. G., Laptev, G. I., and G.A. Cvetkova,On Hadamard correctness of the Cauchy problem for the equation of evolution, Soviet Math. Dokl.11 (1970), 763–766.

    Google Scholar 

  • [M-O-O] Miyadera, I., Oharu, S., and N. Okazawa,Generation theorems of semigroups of linear operators, Publ. Res. Inst. Math. Sci., Kyoto Univ.8 (1973), 509–555.

    Article  MathSciNet  Google Scholar 

  • [Na] Nagel, R.,Sobolev spaces and semigroups, Semesterbericht Funktional-analysis Tübingen, Sommersemester 1984.

  • [Ne1] Neubrander, F.,Integrated semigroups and their applications to the abstract Cauchy problem, Pacific J. Math.135 (1988), 111–155.

    MATH  MathSciNet  Google Scholar 

  • [Ne2] Neubrander, F.,Integrated semigroups and their application to complete second order problems, Semigroup Forum38 (1989), 233–251.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ne3] Neubrander, F.,Abstract elliptic operators, analytic interpolation semigroups, and Laplace transforms of analytic functions, Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 1988/89.

  • [N-S] Neubrander, F., and B. Straub,Fractional powers of operators with polynomially bounded resolvent, Semesterbericht Funktionalysis, Tübingen, Wintersemester 1988/89.

  • [Oh] Oharu, S.,Semigroups of linear operators in a Banach space, Publ. RIMS, Kyoto Univ.7 (1971), 205–260.

    Article  MathSciNet  Google Scholar 

  • [Pa] Pazy, A., “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer Verlag, New-York 1983.

    MATH  Google Scholar 

  • [So] Sova, M.,Problème de Cauchy pour équations hyperboliques opérationnelles à coefficients constants non-bornés, Ann. Scuola Norm. Sup. Pisa,22 (1968), 67–100.

    MATH  MathSciNet  Google Scholar 

  • [T-M1] Tanaka, N., and I. Miyadera,Some remarks on C-semigroups and integrated semigroups, Proc. Japan Acad.63 (1987), 139–142.

    Article  MATH  MathSciNet  Google Scholar 

  • [T-M2] Tanaka, N., and I. Miyadera,Exponentially bounded C-semigroups and integrated semigroups, Tokyo J. Math.12 (1989), 99–115.

    Article  MATH  MathSciNet  Google Scholar 

  • [Th] Thieme, H. R.,Integrated semigroups and integrated solutions to abstract Cauchy problems, J. Math. analysis and Appl.152 (1990), 416–447.

    Article  MATH  MathSciNet  Google Scholar 

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Communicated by R. Nagel

A preliminary version of this paper appeared in: Semesterbericht Funktionalanalysis 15, Tübingen (1988/89).

Research supported in part by NSF Grant DMS-8601983 and by DFG (Deutsche Forschungsgemeinschaft)

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Arendt, W., Neubrander, F. & Schlotterbeck, U. Interpolation of semigroups and integrated semigroups. Semigroup Forum 45, 26–37 (1992). https://doi.org/10.1007/BF03025746

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