no. 4
Finite rank, relatively bounded perturbations of semigroups generators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 12 (1985) no. 4, pp. 641-668. 
@article{ASNSP_1985_4_12_4_641_0,
     author = {Lasiecka, I. and Triggiani, R.},
     title = {Finite rank, relatively bounded perturbations of semigroups generators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {641--668},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 12},
     number = {4},
     year = {1985},
     mrnumber = {848843},
     zbl = {0602.47029},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1985_4_12_4_641_0/}
}
TY  - JOUR
AU  - Lasiecka, I.
AU  - Triggiani, R.
TI  - Finite rank, relatively bounded perturbations of semigroups generators
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1985
SP  - 641
EP  - 668
VL  - 12
IS  - 4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1985_4_12_4_641_0/
LA  - en
ID  - ASNSP_1985_4_12_4_641_0
ER  - 
%0 Journal Article
%A Lasiecka, I.
%A Triggiani, R.
%T Finite rank, relatively bounded perturbations of semigroups generators
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1985
%P 641-668
%V 12
%N 4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1985_4_12_4_641_0/
%G en
%F ASNSP_1985_4_12_4_641_0
Lasiecka, I.; Triggiani, R. Finite rank, relatively bounded perturbations of semigroups generators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 12 (1985) no. 4, pp. 641-668. http://www.numdam.org/item/ASNSP_1985_4_12_4_641_0/

[B-N1] P. Butzer - R. Nessel, Fourier Analysis and Approximations, Vol. 1, Academic Press, New York, 1971. | MR | Zbl

[D1] G. Doetsch, Introduction to the theory and Application of the Laplace transformation, Springer-verlag, New York, Heidelberg, Berlin, 1970. | MR | Zbl

[D-S1] W. Desch - W. Schappacher, On relatively bounded perturbations of linear C0-semigroups, preprint May 1983, Institute für Mathematik, Technische Universität Graz, Austria.

[F1] H.O. Fattorini, The Cauchy Problem, Encyclopedia Math. Appl., Addison-Wesley, 1983. | MR

[H-P1] E. Hille and R. Phillips, Functional Analysis and semigroups, Amer. Math. Soc., Providence, R.I., 1957. | MR | Zbl

[K1] T. Kato, Perturbation Theory of Linear Operators, Springer-Verlag, 1966. | MR | Zbl

[K2] H.O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., vol. XXIII (1970), pp. 277-298. | MR | Zbl

[M1] V.P. Mikhailov, Partial differential equations, MIR Publishers, Moscow (English translation), 1978. | MR | Zbl

[P1] A. Pazy, Semigroups of Operators and Applications to Partial Differential Equations, Lect. Notes # 10, Math. Dept. Univ. of Maryland, College Park (1974). | MR

[L-T1] I. Lasiecka - R. Triggiani, A cosine operator approach to modelling L2(O, T; L2(Γ))-input hyperbolic equations, Appl. Math. Optim., 7 (1981), pp. 35-93. | Zbl

[L-T2] I. Lasiecka - R. Triggiani, Hyperbolic equations with Dirichlet boundary feedback via position vector: regularity and almost periodic stabilization, I, Appl. Math. Optim., 8 (1981), pp. 1-37. | MR | Zbl

[L-T3] I. Lasiecka - R. Triggiani, Dirichlet boundary stabilization of the wave equation with damping feedback of finite range, J. Math. Anal. Appl., 97 (1983), pp. 112-130. | MR

[L-T4] I. Lasiecka - R. Triggiani, Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations, J. Differential Equations, 47 (1983), pp. 246-272. | MR

[L-T5] I. Lasiecka - R. Triggiani, Nondissipative boundary stabilization of the wave equation via boundary observations, J. Math. Pures Appl., 63 (1984), pp. 59-80. | MR

[L-T6] I. Lasiecka - R. Triggiani, Regularity of hyperbolic equations under L2(O, T; L2(Γ))-Dirichtet boundary terms, Appl. Math. Optim., 40 (1983), pp. 275-286. | Zbl

[L-T7] I. Lasiecka - R. Triggiani, Hyperbolic equations with nonhomogeneous Neumann boundary terms. - I: Regularity. To appear.

[L-T8] I. Lasiecka R. Triggiani, Dirichlet boundary control problem for parabolic equations with quadratic cost: analyticity and Riccati's feedback synthesis, SIAM J. Control Optim., 24 (1983), pp. 41-67. | MR | Zbl

[L-T9[ I. Lasiecka - R. Triggiani, Finite rank, relatively bounded perturbations of semi-groups generators. Part II : spectrum and Riesz basis assignment with applications to feedback systems, Ann. Mat. Pura Appl. to appear. | Zbl

[R1] J. Rauch, L2 is a continuable initial condition for Kreiss mixed problems, Comm. Pure Appl. Math., 25 (1972), pp. 265-285. | MR | Zbl

[T1] R. Triggiani, Well posedness and regularity of boundary feedback parabolic systems, J. Differential Equations, 36 (1980), pp. 347-362. | MR | Zbl

[T2[ R. Triggiani, Aε-bounded, finite rank perturbations of a s.c. group generators : counterexamples to generation and to another condition for well-posedness. Lecture Notes in Mathematics 1076, Infinite dimensional systems, Proceedings, Retzholf (1983), Springer-Verlag (1984), pp. 227-253. | Zbl

[Y1] K. Yosida, Functional Analysis, Springer-Verlag, 4th Edition, 1976.