@incollection{AST_2003__284__181_0,
author = {Melin, Anders and Sj\"ostrand, Johannes},
title = {Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension $2$},
booktitle = {Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony},
editor = {Lebeau Gilles},
series = {Ast\'erisque},
pages = {181--244},
year = {2003},
publisher = {Soci\'et\'e math\'ematique de France},
number = {284},
zbl = {1061.35186},
language = {en},
url = {https://www.numdam.org/item/AST_2003__284__181_0/}
}
TY - CHAP AU - Melin, Anders AU - Sjöstrand, Johannes TI - Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension $2$ BT - Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony AU - Collectif ED - Lebeau Gilles T3 - Astérisque PY - 2003 SP - 181 EP - 244 IS - 284 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2003__284__181_0/ LA - en ID - AST_2003__284__181_0 ER -
%0 Book Section %A Melin, Anders %A Sjöstrand, Johannes %T Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension $2$ %B Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony %A Collectif %E Lebeau Gilles %S Astérisque %D 2003 %P 181-244 %N 284 %I Société mathématique de France %U https://www.numdam.org/item/AST_2003__284__181_0/ %G en %F AST_2003__284__181_0
Melin, Anders; Sjöstrand, Johannes. Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension $2$, dans Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony, Astérisque, no. 284 (2003), pp. 181-244. https://www.numdam.org/item/AST_2003__284__181_0/
[BaGrPa] , , , Normal forms and quantization formulae, Comm. Math. Phys. 207 (1) (1999), 173-195. | Zbl | DOI
[BaTu] , , Singularities of normal forms and topology of orbits in area-preserving maps, J. Phys. A, 25 (8) (1992), 427-432. | Zbl | DOI
[BeJoSc] , , , Partial differential equations, Reprint of the 1964 original. Lectures in Applied Mathematics, AMS, Providence, R.I., 1979. | Zbl
[BrCoDu] , , , On the location of resonances for Schrödinger operators in the semiclassical limit. I. Resonance free domains, J. Math. Anal. Appl. 126 (1) (1987), p. 90-99. | Zbl | DOI
[Ca] , Sur les systémes linéaires aux dérivées partielles de premier ordre à deux variables, C.R. Acad. Sci., vol 197 (1933), 471-474. | JFM
[Co] , Quasi-modes sur les variétés Riemanniennes, Inv. Math., 43 (1) (1977), p. 15-52. | Zbl | EuDML | DOI
[DiSj] , , Spectral asymptotics in the semi-classical limit, London Math. Soc. Lecture Notes Series 269, Cambridge University Press 1999. | Zbl
[DuHo] , , Fourier integral operators. II, Acta Math. 128 (1972), 183-269. | Zbl | DOI
[GeSj] , , Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys., 108 (1987), 391-421. | Zbl | DOI
[GrSj] , , Microlocal analysis for differential operators, an introduction, London Math. Soc. Lecture Notes Series 196, Cambridge Univ. Press, 1994. | Zbl
[HeRo] , , Puits de potentiel généralisés et asymptotique semiclassique, Ann. Henri Poincaré, Phys. Th., 41 (3) (1984), 291-331. | Zbl | Numdam | EuDML
[HeSj] , , Résonances en limite semi-classique, Mém. Soc. Math. France (N.S.) No. 24-25, (1986). | MR | Zbl | EuDML | Numdam
[HeSj2] , , Semiclassical analysis for Harper's equation. III. Cantor structure of the spectrum, Mém. Soc. Math. France (N.S.) No. 39 (1989), 1-124. | MR | Zbl | EuDML | Numdam
[KaKe] , , Forme normale de Birkhoff et résonances, Asympt. Anal. 23 (2000), 1-21. | MR | Zbl
[La] , KAM theory and semiclassical approximations to eigenfunctions. With an addendum by A. I. Shnirelman. Ergebnisse der Mathematik und ihrer Grenzgebiete, 24. Springer-Verlag, Berlin, 1993. | MR | Zbl
[Mas] , Théorie des perturbations et méthodes asymptotiques, (translated by J. Lascoux et R. Seneor), Dunod (Paris) (1972). | Zbl
[MeSj] , , Determinants of pseudodifferential operators and complex deformations of phase space, http://xxx.lanl.gov/abs/math.SP/0111292, Methods and Applications of Analysis, to appear. | MR | Zbl
[Mo] , On the generalization of a theorem of A. Liapounoff, Comm. Pure Appl. Math. 11 (1958), 257-271. | MR | Zbl | DOI
[Po1] , Invariant tori, effective stability, and quasimodes with exponentially small error terms. I. Birkhoff normal forms, Ann. Henri Poincaré, Phys. Th., 1 (2) (2000), 223-248. | MR | Zbl | DOI
[Po2] , Invariant tori, effective stability, and quasimodes with exponentially small error terms. II. Quantum Birkhoff normal forms, Ann. Henri Poincaré, Phys. Th., 1 (2) (2000), 249-279. | MR | Zbl | DOI
[Sj1] , Singularités analytiques microlocales, Astérisque, 95 (1982). | MR | Zbl | Numdam
[Sj2] , Semiclassical resonances generated by a non-degenerate critical point, Springer LNM, 1256, 402-429. | MR | Zbl
[Sj3] , Function spaces associated to global -Lagrangian manifolds, pages 369-423 in Structure of solutions of differential equations, Katata/Kyoto, 1995, World Scientific 1996. | MR | Zbl
[Sj4] , Semi-excited states in nondegenerate potential wells, Asymptotic Analysis, 6 (1992), p. 29-43. | MR | Zbl
[Vu] , Invariants symplectiques et semi-classiques des systèmes intégrables avec singularité, Séminaire e.d.p., Ecole Polytechnique, 23 janvier, 2000-2001. | MR | Zbl | Numdam | EuDML







