Characteristic equations for the spectrum of generators

Rainer Nagel

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 24, Issue: 4, page 703-717
  • ISSN: 0391-173X

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Nagel, Rainer. "Characteristic equations for the spectrum of generators." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.4 (1997): 703-717. <http://eudml.org/doc/84275>.

@article{Nagel1997,
author = {Nagel, Rainer},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {characteristic equation; generator; spectrum; perturbation methods; strongly continuous semigroup; delay differential equations; Volterra integro-differential equations; population equations with spatial diffusion; cell population equation},
language = {eng},
number = {4},
pages = {703-717},
publisher = {Scuola normale superiore},
title = {Characteristic equations for the spectrum of generators},
url = {http://eudml.org/doc/84275},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Nagel, Rainer
TI - Characteristic equations for the spectrum of generators
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 24
IS - 4
SP - 703
EP - 717
LA - eng
KW - characteristic equation; generator; spectrum; perturbation methods; strongly continuous semigroup; delay differential equations; Volterra integro-differential equations; population equations with spatial diffusion; cell population equation
UR - http://eudml.org/doc/84275
ER -

References

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  2. [En-1] K.-J. Engel, Systems of evolution equations, Confer. Sem. Mat. Univ. Bari260 (1994), 61-109. Zbl0880.34061MR1385479
  3. [En-2] K.J. Engel, Operator Matrices and Systems of Evolution Equations, Book manuscript 1996. MR1484209
  4. [En-3] K.-J. Engel, Spectral theory and generator property for one-sided coupled operator matrices, Tübinger Berichte zur Funktionalanalysis4 (1994/95), 33-60. 
  5. [Gr] A. Grabosch, Compactness properties and asymptotics of strongly coupled systems, J. Math. Anal. Appl.187 (1994), 411-437. Zbl0841.92013MR1297033
  6. [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. Zbl0643.92017MR934944
  7. [Gy-We] M. Gyllenberg - G. Webb, A nonlinear structured population model oftumor growth with quiescence, J. Math. Biol.28 (1990), 671-694. Zbl0744.92026MR1072714
  8. [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. Zbl0768.34041MR1155350
  9. [Me-Di] J.A.J. Metz - O. Diekmann, The Dynamics of Physiologically Structured Populations, Lect. Notes Biomath.68, Springer-Verlag, 1986. Zbl0614.92014MR860959
  10. [Na-1] R. Nagel, One parameter Semigroups of Positive Operators, Lect. Notes Math. 1184, Springer-Verlag, 1986. Zbl0585.47030MR839450
  11. [Na-2] R. Nagel, Towards a "matrix theory" for unbounded operator matrices, Math. Z. 201 (1989), 57-68. Zbl0672.47001MR990188
  12. [Na-3] R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Analysis89 (1990), 291-302. Zbl0704.47001MR1042212
  13. [Na-4] R. Nagel, Order in pure and applied functional analysis, Atti Sem. Mat. Fis. Univ. Modena40 (1992), 503-517. Zbl0788.47029MR1200303
  14. [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. Zbl0790.45011MR1241671
  15. [Ne] J v. Neerven, The Asymptotic Behaviour of Semigroups of Linear Operators, Operator Theory, Advances Appl. 88, Birkhäuser Verlag, 1996. Zbl0905.47001MR1409370
  16. [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). 
  17. [Pr] J. Prüss, Evolutionary Integral Equations and Applications, Monographs Math. 87, Birkhäuser Verlag, 1993. Zbl0784.45006MR1238939

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