The modulus semigroup for linear delay equations II

Note di Matematica

Volumn 25, Issue 2, 2006, Pages 191-208

  Voigt, Jürgen ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Functional differential equation; Modulus semigroup; Perturbation theory

Indexed keywords

EID: 38149129202     PISSN: 11232536     EISSN: 15900932     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. C. D. Aliprantis, O. Burkinshaw: Positive operators, Academic Press, Orlando 1985.
2. W. Arendt, C. J. K. Batty, M. Hieber, F. Neubrander: Vector-valued Laplace transforms and Cauchy problems, Birkhäuser, Basel 2001.
3. W. Arendt, J. Voigt: Domination of uniformly continuous semigroups, Acta Appl. Math., 27, 27-31 (1992).
4. A. Bátkai, S. Piazzera: Semigroups and linear partial differential equations with delay, J. Math. Anal. Appl., 264, 1-20 (2001).
5. I. Becker, G. Greiner: On the modulus of one-parameter semigroups, Semigroup Forum, 34, 185-201 (1986).
6. S. Boulite, L. Maniar, A. Rhandi, J. Voigt: The modulus semigroup for linear delay equations, Positivity, 8, 1-9 (2004).
7. P. Charissiadis: On the modulus of semigroups generated by operator matrices, Arch. Math., 58, 345-353 (1992).
8. W. Desch, W. Schappacher: On relatively bounded perturbations of linear C0- semigroups, Ann. Sc. Norm. Super. Pisa, Cl. Sci., Ser. 4, 11, 327-341 (1984).
9. K. J. Engel: Spectral theory and generator property of one-sided coupled operator matrices, Semigroup Forum, 58, 267-295 (1999).
10. W. Kerscher, R. Nagel: Positivity and stability for Cauchy problems with delay, In: Lect. Notes Math., 1324, 216-235 (1988).
11. L. Maniar, J. Voigt: Linear delay equations in the Lp-context, Evolution Equations (G. R. Goldstein, R. Nagel, and S. Romanelli, eds.), Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, 234, 319-330, (2003).
12. P. Meyer-Nieberg: Banach lattices, Springer, Berlin 1991.
13. R. Nagel: One-parameter semigroups of positive operators, Springer, Berlin 1986.
14. H. H. Schaefer: Banach lattices and positive operators, Springer, New York 1974.
15. M. Stein, J. Voigt: The modulus of matrix semigroups, Arch.Math., 82, 311-316 (2004).
16. M. Stein, H. Vogt, J. Voigt: The modulus semigroup for linear delay equations III, J. Funct. Anal., 220, 388-400 (2005).
17. J. Voigt: The projection onto the center of operators in a Banach lattice, Math. Zeitschr., 199, 115-117 (1988).
18. J. Voigt: One-parameter semigroups acting simultaneously on different Lp-spaces, Bull. Soc. R. Sci. Liége, 61, 465-470 (1992).