Finite rank, relatively bounded perturbations of semigroups generators

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1. [B-N1] P. Butzer - R. Nessel, Fourier Analysis and Approximations, Vol. 1, Academic Press, New York, 1971. Zbl0217.42603MR510857
2. [D1] G. Doetsch, Introduction to the theory and Application of the Laplace transformation, Springer-verlag, New York, Heidelberg, Berlin, 1970. Zbl0278.44001MR344810
3. [D-S1] W. Desch - W. Schappacher, On relatively bounded perturbations of linear C0-semigroups, preprint May 1983, Institute für Mathematik, Technische UniversitätGraz, Austria. 
4. [F1] H.O. Fattorini, The Cauchy Problem, Encyclopedia Math. Appl., Addison-Wesley, 1983. MR692768
5. [H-P1] E. Hille and R. Phillips, Functional Analysis and semigroups, Amer. Math. Soc., Providence, R.I., 1957. Zbl0078.10004MR89373
6. [K1] T. Kato, Perturbation Theory of Linear Operators, Springer-Verlag, 1966. Zbl0148.12601MR203473
7. [K2] H.O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., vol. XXIII (1970), pp. 277-298. Zbl0188.41102MR437941
8. [M1] V.P. Mikhailov, Partial differential equations, MIR Publishers, Moscow (English translation), 1978. Zbl0388.35002MR498162
9. [P1] A. Pazy, Semigroups of Operators and Applications to Partial Differential Equations, Lect. Notes # 10, Math. Dept. Univ. of Maryland, College Park (1974). MR512912
10. [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. Zbl0473.35022
11. [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. Zbl0479.93052MR646502
12. [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. MR721233
13. [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. MR688105
14. [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. MR776911
15. [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. Zbl0526.35049
16. [L-T7] I. Lasiecka - R. Triggiani, Hyperbolic equations with nonhomogeneous Neumann boundary terms. - I: Regularity. To appear. 
17. [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. Zbl0506.93036MR688439
18. [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. Zbl0623.47040
19. [R1] J. Rauch, L2 is a continuable initial condition for Kreiss mixed problems, Comm. Pure Appl. Math., 25 (1972), pp. 265-285. Zbl0226.35056MR298232
20. [T1] R. Triggiani, Well posedness and regularity of boundary feedback parabolic systems, J. Differential Equations, 36 (1980), pp. 347-362. Zbl0438.35042MR576155
21. [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 Mathematics1076, Infinite dimensional systems, Proceedings, Retzholf (1983), Springer-Verlag (1984), pp. 227-253. Zbl0554.35008
22. [Y1] K. Yosida, Functional Analysis, Springer-Verlag, 4th Edition, 1976.