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Towards a “matrix theory” for unbounded operator matrices

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References

  1. Adams, R.A.: Sobolev Spaces. New York: Academic Press 1975

    Google Scholar 

  2. Amann, H.: Existence and regularity for semilinear parabolic evolution equations. Ann. Scuola Norm. Sup. Pisa11, 593–676 (1984)

    Google Scholar 

  3. Amann, H.: Global existence for semilinear parabolic systems. J. Reine Angew. Math.360, 47–83 (1985)

    Google Scholar 

  4. Brown, D.R., Buoni, J.J.: On the spectrum of operator matrices. Glasnik Mat.21, 357–362 (1986)

    Google Scholar 

  5. Burns, J.A., Herdman, T.L.: Adjoint semigroup theory for a class of functional differential equations. SIAM J. Math. Anal.7, 729–745 (1976)

    Google Scholar 

  6. Chen, G., Grimmer, R.: Semigroups and integral equations. J. Integral Equations2, 133–154 (1980)

    Google Scholar 

  7. Delfour, M.C.: The largest class of hereditary systems defining aC 0-semigroup on the product space. Can. J. Math.32, 969–978 (1980)

    Google Scholar 

  8. Desch, W., Grimmer, R., Schappacher, W.: Wellposedness and wave propagation for a class of integrodifferential equations in Banach space. Preprint 1987

  9. Desch, W., Schappacher, W.: On relatively bounded perturbations of linearC 0-semigroups. Ann. Scuola Norm. Sup. Pisa11, 327–341 (1984)

    Google Scholar 

  10. Desch, W., Schappacher, W.: A semigroup approach to integrodifferential equations in Banach spaces. J. Integral Equations10, 99–110 (1985)

    Google Scholar 

  11. Engel, K.J., Nagel, R.: On the spectrum of certain systems of linear evolution equations. In: Favini, A., Obrecht, E. (eds.): Differential equations in Banach spaces. Proceedings, Bologna 1985. Lect. Notes Math.1223, 102–109. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  12. Goldstein, J.A.: Semigroups of linear operators and applications. Oxford University Press 1985

  13. Halmos, P.R.: A Hilbert space problem book. Berlin Heidelberg New York: Springer 1974

    Google Scholar 

  14. Kellermann, H.: Integrated semigroups. J. Funct. Anal. To appear

  15. Leis, R.: Initial boundary value problems in mathematical physics. Stuttgart: Teubner. New York: J. Wiley 1986

    Google Scholar 

  16. Leugering, G.: A generation result for a class of linear thermo-viscoelastic material. In: Brosowski, B., Martensen, E. (eds.): Dynamical problems in mathematical physics. P. Lang 1983

  17. Miller, R.K.: Linear Volterra integrodifferential equations as semigroups. Funkc. Ekvac.17, 39–55 (1974)

    Google Scholar 

  18. Nagel, R.: Well-posedness and positivity for systems of linear evolution equations. Conferenze Seminario Mat. Univ. Bari203, 1–29 (1985)

    Google Scholar 

  19. Nishida, T., Matsumura, A.: The initial value problem for the equations of motion of compressible, viscous, and heat-conducting fluids. Proc. Jap. Acad., Ser. A55, 337–342 (1979)

    Google Scholar 

  20. Neves, A.F., Souza Ribeiro, H., Lopes, O.: On the spectrum of evolution operators generated by hyperbolic systems. J. Funct. Anal.67, 320–344 (1986)

    Google Scholar 

  21. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  22. Salomon, D.: Control and observation of neutral systems. London: Pitnam Publ. Comp. 1984

    Google Scholar 

  23. Strang, G.: Linear algebra and its applications. San Diego: Harcourt Brace Jovanovich, Publ. 1988

    Google Scholar 

  24. Ströhmer, G.: About the resolvent of an operator from fluid dynamics. Math. Z.194, 183–191 (1987)

    Google Scholar 

  25. Zabczyk, J.: On decomposition of generators. SIAM J. Control Optimization16, 523–534 (1978)

    Google Scholar 

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This work was done during a sabbatical stay at the Tulane University in New Orleans, USA. I gratefully acknowledge the wonderful hospitality and helpful cooperation of J.A. Goldstein

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Nagel, R. Towards a “matrix theory” for unbounded operator matrices. Math Z 201, 57–68 (1989). https://doi.org/10.1007/BF01161994

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