@article{AIHPA_1998__68_1_17_0, author = {Petkov, Vesselin and Popov, Georgi}, title = {Semi-classical trace formula and clustering of eigenvalues for {Schr\"odinger} operators}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {17--83}, publisher = {Gauthier-Villars}, volume = {68}, number = {1}, year = {1998}, mrnumber = {1618918}, zbl = {0919.35095}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1998__68_1_17_0/} }
TY - JOUR AU - Petkov, Vesselin AU - Popov, Georgi TI - Semi-classical trace formula and clustering of eigenvalues for Schrödinger operators JO - Annales de l'I.H.P. Physique théorique PY - 1998 SP - 17 EP - 83 VL - 68 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1998__68_1_17_0/ LA - en ID - AIHPA_1998__68_1_17_0 ER -
%0 Journal Article %A Petkov, Vesselin %A Popov, Georgi %T Semi-classical trace formula and clustering of eigenvalues for Schrödinger operators %J Annales de l'I.H.P. Physique théorique %D 1998 %P 17-83 %V 68 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1998__68_1_17_0/ %G en %F AIHPA_1998__68_1_17_0
Petkov, Vesselin; Popov, Georgi. Semi-classical trace formula and clustering of eigenvalues for Schrödinger operators. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 1, pp. 17-83. http://archive.numdam.org/item/AIHPA_1998__68_1_17_0/
[1] A remark on a priori bound and existence of periodic solutions of hamiltonian systems, Periodic solutions of hamiltonian systems and related topics, NATO ASI Series, Series C, 209, 1987, pp. 85-88. | MR | Zbl
, , and ,[2] A semi-classical trace formula for Schrödinger operators, Commun. Math. Phys., Vol. 136, 1991, pp. 567-584. | MR | Zbl
and ,[3] Rayleigh quasimodes in linear elasticity, Comm. Partial Diff. Equations, Vol. 17, 1992, pp. 1327-1367. | MR | Zbl
and ,[4] A semi-classical trace formula for several commuting operators, Preprint, Université de Nantes, 1996.
and ,[5] Spectre d'un hamiltonien quantique et mécanique classique, Comm. Partial Diff. Equations, Vol. 5, 1980, pp. 595-644. | MR | Zbl
,[6] Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques, Comment. Math. Helv., Vol. 54, 1979, pp. 508-522. | MR | Zbl
,[7] Opérateurs h-pseudo-différentiels à flot périodique et asymptotique semi-classique, Thèse de Doctorat, Université Paris XIII, 1994.
,[8] Oscillatory integrals, Lagrange immersions and infolding of singularities, Comm. in Pure and Appl. Math., Vol. 27, 1974, pp. 207-281. | MR | Zbl
,[9] The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math., Vol. 29, 1975, 39-79. | MR | Zbl
and ,[10] On the period spectrum of a symplectic map, J. Funct. Anal., Vol. 100, 1991, pp. 317-358. | MR | Zbl
and ,[11] Circular symmetry and the trace formula, Invent. Math., Vol. 96, 1989, pp. 385-423. | MR | Zbl
and ,[12] Sharp asymptotics of the spectrum of the Laplace operator on a manifold with periodic geodesics, Trudy Matem. Inst. Steklov, Vol. 179, 1988 (in Russian), English transl. in Proc. Steklov Institute of Mathematics, Vol. 179, 1989, pp. 35-53. | MR | Zbl
and ,[13] Periodic orbits and classical quantization condition, J. Math. Phys., Vol. 12, 1971, pp. 345-358.
,[14] Ergodicité et limite semi-classique, Commun. Math. Phys., Vol. 109, 1987, pp. 313-326. | MR | Zbl
, and ,[15] Propriétes asymptotiques du spectre d'opérateurs pseudo-différentieles sur Rn, Comm. Partial Diff. Equations, Vol. 7, 1982, pp. 795-882. | MR | Zbl
and ,[16] Calcul fonctionnel par la transformation de Mellin, J. Funct. Anal., Vol. 53, 1983, pp. 246-268. | MR | Zbl
and ,[17] Symplectic Invariants and Hamiltonian Dynamics, Birkhäser, Basel, 1994. | MR | Zbl
and ,[ 18] Fourier integral operators I, Acta Math. Vol. 127, 1971, pp. 79-183. | MR | Zbl
,[19] The Analysis of Linear Partial Differential Operators III, Springer, Berlin - Heidelberg - New York, 1985. | MR | Zbl
,[20] The Analysis of Linear Partial Differential Operators IV, Springer, Berlin - Heidelberg - New York, 1985. | MR
,[21] Semi-classical microlocal analysis and precise spectral asymptotics, Ecole Polytechnique, Centre de Mathématiques, Preprints 1, 2, 3, 1991.
,[22] Semiclassical principal symbols and Gutzwiller's trace formula, Reports on Mathematical Physics, Vol. 31, 1992, pp. 279-295. | MR | Zbl
,[23] Sur la formule semi-classique des traces, C. R, Acad. Sci. Paris, t. 313, Série I, 1991, pp. 217-222. | MR | Zbl
et ,[24] On the Lebesgue measure of the periodic points of a contact manifold, Math. Z., Vol. 218, 1995, pp. 91-102. | MR | Zbl
and ,[25] Une formule de trace semi-classique et asymptotiques de valeurs propres de l'opérateur de Schrödinger, C. R. Acad. Sci. Paris, t. 323, Série I, 1996, pp. 163-168. | MR | Zbl
et ,[26] Asymptotiques semi-clasiques du spectre d'hamiltoniens quantiques et trajectoires classiques périodiques, Comm Part. Diff. Equations, Vol. 10, 1985, pp. 365-390. | MR | Zbl
and ,[27] Length spectrum invariants of Riemannian manifolds, Math. Z., Vol. 213, 1993, pp. 311-351. | MR | Zbl
,[28] Asymptotics of the spectrum of a pseudodifferential operator with periodic characteristics, Zap. Nauchn. Sem. Leningrad. Otdel Mat. Inst. Steklov (LOMI). vol. 152. 1986, pp. 94-104 (in Russian), English translation in J. Soviet Math., Vol. 40, 1988. pp. 645-652. | MR | Zbl
,[29] Exact asymptotics of the spectrum of a boundary value problem and periodic billiards. Izv. AN SSSR, Ser. Mat,. Vol. 52, 1988, pp. 1230-1251 (in Russian), English translation in Math. USSR Izvestiya, Vol. 33, 1989, pp. 553-573. | MR | Zbl
,[30] Branching Hamiltonian billiards, Doklady Akad. Nauk SSSR, Vol. 301, 1988, pp. 271-274, English translation, Soviet Math. Dokl., Vol. 38, 1989, pp. 64-68. | MR | Zbl
and ,[31] Spectral statistics on Zoll surfaces, Commun. Math. Pxhysics, Vol. 154, 1993, pp. 313-346. | MR | Zbl
and ,[32] On the hypotheses of Rabinowitz' periodic orbit theorems, J. Diff. Equations, Vol. 33, 1979, pp. 353-358. | MR | Zbl
,[33] Kuznecov sum formulae and Szegö limit formulae on manifolds, Comm. Partial Diff. Equations, Vol. 17, 1992, pp. 221-260. | MR | Zbl
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