On multiplicative perturbation of integral resolvent families

Journal of Mathematical Analysis and Applications

Volumn 327, Issue 2, 2007, Pages 1335-1359

  Lizama, Carlos ^a   Poblete, Verónica ^a  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Favard spaces; Integral resolvent families; Multiplicative perturbation; Resolvent families

Indexed keywords

EID: 33751012102     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.04.087     Document Type: Article

References (24)

1. Chang J.-C., and Shaw S.-Y. Perturbation theory of abstract Cauchy problems and Volterra equations. Nonlinear Anal. 30 (1997) 3521-3528
2. Chang J.-C., and Shaw S.-Y. Multiplicative and additive perturbations of resolvent families. Int. Math. J. 2 (2002) 841-853
3. Clément P., Diekmann O., Gyllenberg M., Heijmans H.J.A.M., and Thieme H.R. Perturbation theory for dual semigroups: The sun-reflexive case. Math. Ann. 277 (1987) 709-725
4. Desch W., and Schappacher W. Some generation results for perturbed semigroups. In: Clement Ph., et al. (Ed). Semigroup Theory and Applications, Proc. Conf. Trieste/Italy 1987. Lect. Notes Pure Appl. Math. vol. 116 (1989), Dekker, New York 125-152
5. Dorroh J.R., and Holderrieth A. Multiplicative perturbation of semigroups generators. Boll. Unione Mat. Ital. Sez. A (7) 7 (1993) 47-57
6. Dorroh B. Contraction semigroups in a function space. Pacific J. Math. 19 (1966) 35-38
7. Greiner G. Perturbing the boundary conditions of a generator. Houston J. Math. 13 2 (1987) 213-229
8. Grimmer R., and Prüss J. On linear Volterra equations in Banach spaces. Comput. Math. Appl. 11 1-3 (1985) 189-205
9. Gripenberg G., Londen S.-O., and Staffans O. Volterra Integral and Functional Equations. Encyclopedia Math. Appl. vol. 34 (1990), Cambridge University Press, Cambridge
10. Gustafson K.G. A note on left multiplication of semigroup generators. Pacific J. Math. 24 (1968) 463-465
11. Gustafson K., and Lumer G. Multiplicative perturbation of semigroup generators. Pacific J. Math. 41 (1972) 731-742
12. Engel K.-J., and Nagel R. One Parameter Semigroups for Linear Evolution Equations. Grad. Texts in Math. vol. 194 (2000), Springer, Berlin
13. Lizama C. Regularized solutions for abstract Volterra equations. J. Math. Anal. Appl. 243 (2000) 278-292
14. Lizama C. On approximation and representation of k-regularized resolvent families. Integral Equations Operator Theory 41 2 (2001) 223-229
15. Lizama C., and Prado H. Rates of approximation and ergodic limits of regularized operator families. J. Approx. Theory 122 1 (2003) 42-61
16. Lizama C., and Sánchez J. On perturbation of k-regularized resolvent families. Taiwanese J. Math. 7 2 (2003) 217-227
17. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci. vol. 44 (1983), Springer-Verlag
18. 0-semigroups and applications to step responses and cumulative outputs. J. Funct. Anal. 128 (1995) 315-340
19. Piskarev S., and Shaw S.-Y. Perturbation and comparison of cosine functions. Semigroup Forum 51 (1995) 225-246
20. Prüss J. Evolutionary Integral Equations and Applications. Monogr. Math. vol. 87 (1993), Birkhäuser Verlag
21. Rhandi A. Multiplicative perturbation of linear Volterra equations. Proc. Amer. Math. Soc. 119 2 (1993)
22. Travis C.C., and Webb G.F. Cosine families and abstract nonlinear second order differential equations. Acta Math. Acad. Sci. Hung. 32 (1978) 75-96
23. Xiao T.-J., Liang J., and Van Casteren J. Time dependent Desch-Schappacher type perturbations of Volterra integral equations. Integral Equations Operator Theory 44 (2002) 494-506
24. Zabczyk J. On decomposition of generators. SIAM J. Control Optim. 16 4 (1978)