RAGE theorem for power bounded operators and decay of local energy for moving obstacles
Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 2, pp. 155-185. 
@article{AIHPA_1989__51_2_155_0,
     author = {Petkov, Vesselin M. and Georgiev, Vladimir S.},
     title = {RAGE theorem for power bounded operators and decay of local energy for moving obstacles},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {155--185},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {2},
     year = {1989},
     mrnumber = {1033615},
     zbl = {0705.35094},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1989__51_2_155_0/}
}
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Petkov, Vesselin M.; Georgiev, Vladimir S. RAGE theorem for power bounded operators and decay of local energy for moving obstacles. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 2, pp. 155-185. http://www.numdam.org/item/AIHPA_1989__51_2_155_0/

[1] A. Bachelot and V. Petkov, Existence des opérateurs d'ondes pour les systèmes hyperboliques avec un potentiel périodique en temps, Ann. Inst. Henri Poincaré (Physique théorique) t. 47, n° 4, 1987, pp. 383-428. | Numdam | MR | Zbl

[2] J. Cooper and W. Strauss, Energy Boundness and Local Energy Decay of Waves Reflecting off a Moving Obstacle, Indiana Univ. Math. J., t. 25, 1976, pp. 671-690. | MR | Zbl

[3] J. Cooper and W. Strauss, Representation of the Scattering Operator for Moving Obstacles, Indiana Univ. Math. J., t. 28, 1979, pp. 643-671. | MR | Zbl

[4] J. Cooper and W. Strauss, Scattering of Waves by Periodically Moving Bodies, J. Funct. Anal., t, 47, 1982, pp. 180-229. | MR | Zbl

[5] J. Cooper and W. Strauss, Abstract Scattering Theory for Time Periodic Systems with Applications to Electromagnetism, Indiana Univ. Math. J., t. 34, 1985, pp. 33-83. | MR | Zbl

[6] J. Cooper and W. Strauss, The Initial Boundary Problem for the Maxwell Equations in the Presence of a Moving Body, S.I.A.M. J. Math. Anal., t. 16, No. 6, 1985, pp. 1165-1179. | MR | Zbl

[7] N. Dunford and J. Schwartz, Linear Operators, Part III, Spectral Operators, Wiley Interseciences, New York, 1971. | MR | Zbl

[8] V. Georgiev and V. Petkov, Théorème de type RAGE pour des opérateurs à puissances bornées, C.R. Acad. Sci. Paris, T. 303, série I, 1986, pp. 605-608. | MR | Zbl

[9] V. Georgiev, Uniform Boundness of the Energy for Time Periodic Potentials, Conference on Operator Theory, Timichoara, 1988, (to appear). | MR | Zbl

[10] L. Hörmander, The Analysis of Linear Partial Differential Operators III, Springer-Verlag, Berlin, Heidelberg, 1985. | MR | Zbl

[11] P. Lax and R. Phillips, Scattering Theory, Academic Press, 1967. | Zbl

[12] P. Lax and R. Phillips, Scattering Theory for the Acoustical Equation in an Even Number of Space Dimensions, Indiana Univ, Math. J., t. 22, 1972, pp. 101-134. | MR | Zbl

[13] P. Lax and R. Phillips, Scattering Theory for Dissipative Systems, J. Funct. Anal., t. 14, 1973, pp. 172-233. | Zbl

[14] R. Melrose, Singularities and Energy Decay in Acoustical Scattering, Duke Math. J., T. 46, 1979, pp. 43-59. | MR | Zbl

[15] R. Melrose and J. Sjöstrand, Singularities of Boundary Value Problems I, II, Comm. Pure Appl. Math., t. 31, 1978, pp. 593-617; t. 35, 1982, pp. 129-168. | MR | Zbl

[16] C. Morawetz, J. Ralston and W. Strauss, Decay of Solutions of the Wave Equation Outside Non-Tapping Obstacles, Comm. Pure Appl. Math., t. 30, 1977, pp. 447-508. | MR | Zbl

[17] V. Petkov, Scattering Theory for Mixed Problems in the Exteriour of Moving Obstacles, pp. 141-155 in Hyperbolic Equations, F. COLOMBINI and M. K. V. MURTHY Ed., Pitman Research Notes in Mathematics Series, 158, Longman Scientific & Technical, 1987. | Zbl

[18] V. Petkov, Les problèmes inverses de diffusion pour les perturbations dépendant du temps, Séminaire Équations aux Dérivées Partielles, Exposé n° XX, École Polytechnique, 1987-1988. | EuDML | Numdam | MR | Zbl

[19] V. Petkov, Scattering Theory for Hyperbolic Operators, North-Holland, Amsterdam, 1989. | Zbl

[20] G. Popov and Tzv. Rangelov, On the Exponential Growth of the Local Energy for Periodically Moving Obstacles, Osana J. Math. (to appear). | Zbl

[21] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. III, Scattering Theory, Academic Press, New York, 1979. | MR | Zbl

[22] B. Simon, Phase Space Analysis of Simple Scattering Systems: Extension of Some Work of Enss, Duke Math. J., t. 46, 1979, pp. 119-168. | MR | Zbl

[23] W. Strauss, The Existence of the Scattering Operator for Moving Obstacles, J. Funct. Anal., t. 31, 1979, pp. 255-262. | MR | Zbl

[24] B.R. Vainberg, Asymptotic Methods for the Equations of the Mathematical Physics, Moscow University, 1982 (in Russian). | MR | Zbl