Spectral theory and generator property for one-sided coupled operator matrices

Semigroup Forum

Volumn 58, Issue 2, 1999, Pages 267-295

  Engel, Klaus Jochen ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000080138     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002339900020     Document Type: Article

References (30)

1. Burns, J. A. and R. H. Fabiano, Modeling and approximation for a viscoelastic control problem, Distributed Parameter Systems, Lect. Notes in Control and Inf. Sci. vol. 102, Springer-Verlag, 1987, pp. 23-39.
2. Burns, J. A. and R. H. Fabiano, Feedback control of a hyperbolic partial-differential equation with viscoelastic damping, Control Theory Adv. Tech. 5 (1989), 157-188.
3. Burns, J. A., T. L. Herdman, and H. W. Stech, Linear functional differential equations as semigroups on product spaces, SIAM J. Math. Anal. 14 (1983), 98-116.
4. Butzer, P. and H. Behrens, "Semigroups of Operators and Approximation", Springer-Verlag, 1967.
5. Chen, G. and R. Grimmer, Semigroups and integral equations, J. Integral Equations 2 (1980), 133-154.
6. Desch, W., R. Grimmer, and W. Schappacher, Well posedness and wave propagation for a class of integrodifferential equations in Banach space, J. Differential Equations 74 (1988), 391-411.
7. Desch, W. and W. Schappacher, A semigroup approach to integrodifferential equations in Banach spaces, J. Integral Equations 10 (1985), 99-110.
8. Desch, W. and W. Schappacher, Some perturbation results for analytic semigroups, Math. Ann. 281 (1988), 157-162.
9. Desch, W. and W. Schappacher, Some generation results for perturbed semigroups, Semigroup Theory and Applications (Proceedings Trieste 1987) (P. Clément, S. Invernizzi, E. Mitidieri, and I.I. Vrabie, eds.), Lect. Notes in Pure and Appl. Math, vol. 116, Marcel Dekker, 1989, pp. 125-152.
10. Doetsch, G., "Einführung in die Theorie und Anwendung der Laplace-Transformation", Birkhäuser Verlag, 1970.
11. Eberhardt, B., "Operator matrices as generators of semigroups", Ph.D. thesis, Universität Tübingen, 1994.
12. Engel, K.-J., "Operator matrices and systems of evolution equations", Habilitationsschrift, Universität Tübingen, 1995.
13. Förster, K.-H. and E.-O. Liebetrau, On semi-Fredholm operators and the conjugate of a product of operators, Studia Math. LIX (1977), 301-306.
14. Goldstein, J. A., "Semigroups of Operators and Applications", Oxford University Press, 1985.
15. Grimmer, R. and W. Schappacher, Integrodifferential equations in Banach space with infinite memory, Volterra Integrodifferential Equations in Banach Spaces and Applications (Proceedings Trento 87) (G. Da Prato and M. Iannelli, eds.), Pitman Res. Notes Math. Ser. vol. 190, Pitman, 1989, pp. 167-176.
16. Hennig, B. and F. Neubrander, On representations, inversions, and approximations of Laplace transforms in Banach spaces, Appl. Anal. 49 (1993), 151-170.
17. Holderrieth, A., "Multiplicative Perturbations", Ph.D. thesis, Universität Tübingen, 1992.
18. Kappel, F., Semigroups and delay equations, Semigroups, Theory and Applications-II (Proceedings Trieste 84) (H. Brezis, M. Crandall, and F. Kappel, eds.), Pitman Res. Notes Math. Ser. vol. 152, Pitman, 1986, pp. 136-176.
19. Kappel, F. and K. pei Zhang, Equivalence of functional-differential equations of neutral type and abstract Cauchy problems, Mh. Math. 101 (1986), 115-133.
20. Miller, R. K., Linear Volterra integrodifferential equations as semigroups, Funkcial. Ekvac. 17 (1974), 39-55.
21. Nagel, R., (ed.), "One-parameter Semigroups of Positive Operators", Lect. Notes in Math. vol. 1184, Springer-Verlag, 1986.
22. Nagel, R., Towards a "matrix theory" for unbounded operator matrices, Math. Z. 201 (1989), 57-68.
23. Nagel R., The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal. 89 (1990), 291-302.
24. Nagel, R., G. Nickel, and S. Romanelli, Identification of extrapolation spaces for unbounded operators, Quaestiones Math. (1995), to appear.
25. Nagel R., and E. Sinestrari, Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, Functional Analysis (Proceedings Essen 1991) (K.D. Bierstedt, A. Pietsch, W.M. Ruess, and D. Vogt, eds.), Lect. Notes in Pure and Appl. Math. vol. 150, Marcel Dekker, 1993, pp. 51-70.
26. Neubrander, F., Well-posedness of higher order abstract Cauchy problems, Trans. Amer. Math. Soc. 295 (1986), 257-290.
27. Pazy, A., "Semigroups of Linear Operators and Applications to Partial Differential Equations", Springer-Verlag, 1983.
28. Schechter, M., The conjugate of a product of operators, J. Funct. Anal. 6 (1970), 26-28.
29. Tadmor, G. and J. Turi, Neutral equations and associated semigroups, J. Differential Equations 116 (1995), 59-87.
30. van Neerven, J., "The Adjoint of a Semigroup", Lect. Notes in Math. vol. 1529, Springer-Verlag, 1992.