Characteristic equations for the spectrum of generators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 24 (1997) no. 4, p. 703-717 
@article{ASNSP_1997_4_24_4_703_0,
     author = {Nagel, Rainer J.},
     title = {Characteristic equations for the spectrum of generators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 24},
     number = {4},
     year = {1997},
     pages = {703-717},
     zbl = {0912.47023},
     mrnumber = {1627330},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_24_4_703_0}
}

Nagel, Rainer. Characteristic equations for the spectrum of generators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 24 (1997) no. 4, pp. 703-717. http://www.numdam.org/item/ASNSP_1997_4_24_4_703_0/

[Ar] W. Arendt, Spectrum and growth of positive semigroups, In: G. Ferreyra - G. Ruiz Goldstein - F. Neubrander (eds.): Evolution Equations, Lect. Notes Pure Appl. Math. 168, 21-28, Marcel Dekker, 1995. | MR 1300417 | Zbl 0834.47031

[En-1] K.-J. Engel, Systems of evolution equations, Confer. Sem. Mat. Univ. Bari 260 (1994), 61-109. | MR 1385479 | Zbl 0880.34061

[En-2] K.J. Engel, Operator Matrices and Systems of Evolution Equations, Book manuscript 1996. | MR 1484209

[En-3] K.-J. Engel, Spectral theory and generator property for one-sided coupled operator matrices, Tübinger Berichte zur Funktionalanalysis 4 (1994/95), 33-60.

[Gr] A. Grabosch, Compactness properties and asymptotics of strongly coupled systems, J. Math. Anal. Appl. 187 (1994), 411-437. | MR 1297033 | Zbl 0841.92013

[Gr-Na] G. Greiner - R. Nagel, Growth of cell populations via one-parameter semigroups of positive operators, In: J. A. Goldstein - S. Rosencrans - G. Sod (eds.): Mathematics Applied to Science, 79-105, Academic Press, 1988. | MR 934944 | Zbl 0643.92017

[Gy-We] M. Gyllenberg - G. Webb, A nonlinear structured population model oftumor growth with quiescence, J. Math. Biol. 28 (1990), 671-694. | MR 1072714 | Zbl 0744.92026

[Ka-VL] M.A. Kaashoek - S.M. Verduyn Lunel, Characteristic matrices and spectral properties of evolutionary systems, Trans. Amer. Math. Soc. 334 (1992), 479-517. | MR 1155350 | Zbl 0768.34041

[Me-Di] J.A.J. Metz - O. Diekmann, The Dynamics of Physiologically Structured Populations, Lect. Notes Biomath. 68, Springer-Verlag, 1986. | MR 860959 | Zbl 0614.92014

[Na-1] R. Nagel, One parameter Semigroups of Positive Operators, Lect. Notes Math. 1184, Springer-Verlag, 1986. | MR 839450 | Zbl 0585.47030

[Na-2] R. Nagel, Towards a "matrix theory" for unbounded operator matrices, Math. Z. 201 (1989), 57-68. | MR 990188 | Zbl 0672.47001

[Na-3] R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Analysis 89 (1990), 291-302. | MR 1042212 | Zbl 0704.47001

[Na-4] R. Nagel, Order in pure and applied functional analysis, Atti Sem. Mat. Fis. Univ. Modena 40 (1992), 503-517. | MR 1200303 | Zbl 0788.47029

[Na-Si] R. Nagel - E. Sinestrari, Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, In: K. D. Bierstedt - A. Pietsch - W. M. Ruess - D. Vogt (eds.): Functional Analysis, Lect. Notes Pure Appl. Math. 150, 51-70, Marcel Dekker, 1993. | MR 1241671 | Zbl 0790.45011

[Ne] J V. Neerven, The Asymptotic Behaviour of Semigroups of Linear Operators, Operator Theory, Advances Appl. 88, Birkhäuser Verlag, 1996. | MR 1409370 | Zbl 0905.47001

[Ni-Rh] G. Nickel - A. Rhandi, On the essential spectral radius of semigroups generated by perturbations of Hille-Yosida operators, Differential Integral Equations (to appear).

[Pr] J. Prüss, Evolutionary Integral Equations and Applications, Monographs Math. 87, Birkhäuser Verlag, 1993. | MR 1238939 | Zbl 0784.45006