Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2
Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony, Astérisque, no. 284 (2003), pp. 181-244.
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {284},
     year = {2003},
     zbl = {1061.35186},
     language = {en},
     url = {http://archive.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  - http://archive.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 http://archive.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. http://archive.numdam.org/item/AST_2003__284__181_0/

[BaGrPa] D. Bambusi, S. Graffi, T. Paul, Normal forms and quantization formulae, Comm. Math. Phys. 207 (1) (1999), 173-195. | DOI | Zbl

[BaTu] A. Bazzani, G. Turchetti, Singularities of normal forms and topology of orbits in area-preserving maps, J. Phys. A, 25 (8) (1992), 427-432. | DOI | Zbl

[BeJoSc] L. Bers, F. John, M. Schechter, Partial differential equations, Reprint of the 1964 original. Lectures in Applied Mathematics, AMS, Providence, R.I., 1979. | Zbl

[BrCoDu] P. Briet, J. M. Combes, P. Duclos, 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. | DOI | Zbl

[Ca] Carleman, Sur les systémes linéaires aux dérivées partielles de premier ordre à deux variables, C.R. Acad. Sci., vol 197 (1933), 471-474. | JFM

[Co] Y. Colin De Verdière, Quasi-modes sur les variétés Riemanniennes, Inv. Math., 43 (1) (1977), p. 15-52. | DOI | EuDML | Zbl

[DiSj] M. Dimassi, J. Sjöstrand, Spectral asymptotics in the semi-classical limit, London Math. Soc. Lecture Notes Series 269, Cambridge University Press 1999. | Zbl

[DuHo] J. J. Duistermaat, L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), 183-269. | DOI | Zbl

[GeSj] C. Gérard, J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys., 108 (1987), 391-421. | DOI | Zbl

[GrSj] A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators, an introduction, London Math. Soc. Lecture Notes Series 196, Cambridge Univ. Press, 1994. | Zbl

[HeRo] B. Helffer, D. Robert, Puits de potentiel généralisés et asymptotique semiclassique, Ann. Henri Poincaré, Phys. Th., 41 (3) (1984), 291-331. | EuDML | Numdam | Zbl

[HeSj] B. Helffer, J. Sjöstrand, Résonances en limite semi-classique, Mém. Soc. Math. France (N.S.) No. 24-25, (1986). | EuDML | Numdam | MR | Zbl

[HeSj2] B. Helffer, J. Sjöstrand, Semiclassical analysis for Harper's equation. III. Cantor structure of the spectrum, Mém. Soc. Math. France (N.S.) No. 39 (1989), 1-124. | EuDML | Numdam | MR | Zbl

[KaKe] N. Kaidi, Ph. Kerdelhué, Forme normale de Birkhoff et résonances, Asympt. Anal. 23 (2000), 1-21. | MR | Zbl

[La] V. F. Lazutkin, 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] V. P Maslov, Théorie des perturbations et méthodes asymptotiques, (translated by J. Lascoux et R. Seneor), Dunod (Paris) (1972). | Zbl

[MeSj] A. Melin, J. Sjöstrand, 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] J. Moser, On the generalization of a theorem of A. Liapounoff, Comm. Pure Appl. Math. 11 (1958), 257-271. | DOI | MR | Zbl

[Po1] G. Popov, 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. | DOI | MR | Zbl

[Po2] G. Popov, 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. | DOI | MR | Zbl

[Sj1] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, 95 (1982). | Numdam | MR | Zbl

[Sj2] J. Sjöstrand, Semiclassical resonances generated by a non-degenerate critical point, Springer LNM, 1256, 402-429. | MR | Zbl

[Sj3] J. Sjöstrand, Function spaces associated to global I-Lagrangian manifolds, pages 369-423 in Structure of solutions of differential equations, Katata/Kyoto, 1995, World Scientific 1996. | MR | Zbl

[Sj4] J. Sjöstrand, Semi-excited states in nondegenerate potential wells, Asymptotic Analysis, 6 (1992), p. 29-43. | MR | Zbl

[Vu] S. Vu-Ngoc, Invariants symplectiques et semi-classiques des systèmes intégrables avec singularité, Séminaire e.d.p., Ecole Polytechnique, 23 janvier, 2000-2001. | EuDML | Numdam | MR | Zbl