In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds
Dans ce travail nous étendons un travail précédent sur l’asymptotique de Weyl de la distribution des valeurs propres d’opérateurs différentiels avec des perturbations multiplicatives aléatoires petites, en traitant le cas des opérateurs sur des variétés compactes.
@article{AFST_2010_6_19_2_277_0, author = {Johannes Sj\"ostrand}, title = {Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {277--301}, publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 19}, number = {2}, year = {2010}, doi = {10.5802/afst.1244}, mrnumber = {2674764}, zbl = {1206.35267}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1244/} }
TY - JOUR AU - Johannes Sjöstrand TI - Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2010 SP - 277 EP - 301 VL - 19 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1244/ DO - 10.5802/afst.1244 LA - en ID - AFST_2010_6_19_2_277_0 ER -
%0 Journal Article %A Johannes Sjöstrand %T Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 277-301 %V 19 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1244/ %R 10.5802/afst.1244 %G en %F AFST_2010_6_19_2_277_0
Johannes Sjöstrand. Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 2, pp. 277-301. doi : 10.5802/afst.1244. https://afst.centre-mersenne.org/articles/10.5802/afst.1244/
[1] W. Bordeaux Montrieux, Loi de Weyl presque sûre et résolvante pour des opérateurs différentiels non-autoadjoints, Thesis, CMLS, Ecole Polytechnique, 2008. http://pastel.paristech.org/5367/
[2] W. Bordeaux Montrieux, J. Sjöstrand, Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds, Ann. Fac. Sci. Toulouse, to appear. http://arxiv.org/abs/0903.2937
[3] M. Dimassi, J. Sjöstrand, Spectral asymptotics in the semi-classical limit, London Math. Soc. Lecture Notes Ser., 268, Cambridge Univ. Press, (1999). | MR | Zbl
[4] I.C. Gohberg, M.G. Krein, Introduction to the theory of linear non-selfadjoint operators, Translations of mathematical monographs, Vol 18, AMS, Providence, R.I. (1969). | MR | Zbl
[5] A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators, London Math. Soc. Lecture Notes Ser., 196, Cambridge Univ. Press, (1994). | MR | Zbl
[6] M. Hager, Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints. I. Un modèle, Ann. Fac. Sci. Toulouse Math. (6)15(2)(2006), 243–280. | Numdam | MR | Zbl
[7] M. Hager, Instabilité spectrale semiclassique d’opérateurs non-autoadjoints. II. Ann. Henri Poincaré, 7(6)(2006), 1035–1064. | MR | Zbl
[8] M. Hager, J. Sjöstrand, Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators, Math. Annalen, 342(1)(2008), 177–243. | MR | Zbl
[9] L. Hörmander, Fourier integral operators I, Acta Math., 127(1971), 79–183. | MR | Zbl
[10] A. Iantchenko, J. Sjöstrand, M. Zworski, Birkhoff normal forms in semi-classical inverse problems, Math. Res. Lett. 9(2-3)(2002), 337–362. | MR | Zbl
[11] A. Melin, J. Sjöstrand, Determinants of pseudodifferential operators and complex deformations of phase space. Methods and Applications of Analysis, 9(2)(2002), 177-238. | MR | Zbl
[12] D. Robert, Autour de l’approximation semi-classique, Progress in Mathematics, 68. Birkhäuser Boston, Inc., Boston, MA, 1987. | MR | Zbl
[13] R.T. Seeley, Complex powers of an elliptic operator. 1967 Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) pp. 288–307 Amer. Math. Soc., Providence, R.I. | MR | Zbl
[14] J. Sjöstrand, Resonances for bottles and trace formulae, Math. Nachr., 221(2001), 95–149. | MR | Zbl
[15] J. Sjöstrand, Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations, Annales Fac. Sci. Toulouse, 18(4)(2009), 739–795. | EuDML | Numdam | MR | Zbl
[16] J. Sjöstrand, M. Zworski, Fractal upper bounds on the density of semiclassical resonances, Duke Math J, 137(3)(2007), 381-459. | MR | Zbl
[17] J. Sjöstrand, M. Zworski, Elementary linear algebra for advanced spectral problems, Annales Inst. Fourier, 57(7)(2007), 2095–2141. | EuDML | Numdam | MR | Zbl
[18] J. Wunsch, M. Zworski, The FBI transform on compact manifolds, Trans. A.M.S., 353(3)(2001), 1151–1167. | MR | Zbl
Cited by Sources: