zbMATH — the first resource for mathematics

Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations. (English) Zbl 1194.47058
From the abstract: In this work, we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-selfadjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in arbitrary dimension. We were led to quite essential improvements of many of the probabilistic aspects.

47G30 Pseudodifferential operators
35S30 Fourier integral operators applied to PDEs
Full Text: DOI Numdam EuDML
[1] Bordeaux-Montrieux (W.).— Loi de Weyl presque sûre et résolvante pour des opérateurs différentiels non-autoadjoints, Thesis, CMLS, Ecole Polytechnique, 2008. http://pastel.paristech.org/5367/.
[2] Dimassi (M.), Sjöstrand (J.).— Spectral asymptotics in the semi-classical limit, London Math. Soc. Lecture Notes Ser., 268, Cambridge Univ. Press, (1999). · Zbl 0926.35002
[3] Gohberg (I.C.), Krein (M.G.).— Introduction to the theory of linear non-selfadjoint operators, Translations of mathematical monographs, Vol 18, AMS, Providence, R.I. (1969). · Zbl 0181.13504
[4] Grigis (A.), Sjöstrand (J.).— Microlocal analysis for differential operators, London Math. Soc. Lecture Notes Ser., 196, Cambridge Univ. Press, (1994). · Zbl 0804.35001
[5] Hager (M.).— Instabilité spectrale semiclassique pour des opérateurs non-autoadjoints. I. Un modèle, Ann. Fac. Sci. Toulouse Math. (6)15(2), p. 243-280 (2006). · Zbl 1131.34057
[6] Hager (M.).— Instabilité spectrale semiclassique d’opérateurs non-autoadjoints. II. Ann. Henri Poincaré, 7(6), p. 1035-1064 (2006). · Zbl 1115.81032
[7] Hager (M.), Sjöstrand (J.).— Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators, Math. Annalen, 342(1), p. 177-243 (2008). · Zbl 1151.35063
[8] Hörmander (L.).— Fourier integral operators I, Acta Math., 127, p. 79-183 (1971). · Zbl 0212.46601
[9] Iantchenko (A.), Sjöstrand (J.), Zworski (M.).— Birkhoff normal forms in semi-classical inverse problems, Math. Res. Lett. 9(2-3), p. 337-362 (2002). · Zbl 1258.35208
[10] Seeley (R.T.).— Complex powers of an elliptic operator. 1967 Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) p. 288-307 Amer. Math. Soc., Providence, R.I. · Zbl 0159.15504
[11] Sjöstrand (J.).— Resonances for bottles and trace formulae, Math. Nachr., 221, p. 95-149 (2001). · Zbl 0979.35109
[12] Sjöstrand (J.), Vodev (G.).— Asymptotics of the number of Rayleigh resonances, Math. Ann. 309, p. 287-306 (1997). · Zbl 0890.35098
[13] Sjöstrand (J.), Zworski (M.).— Fractal upper bounds on the density of semiclassical resonances, Duke Math J, 137(3), p. 381-459 (2007). · Zbl 1201.35189
[14] Sjöstrand (J.), Zworski (M.).— Elementary linear algebra for advanced spectral problems, Annales Inst. Fourier, 57(7), p. 2095-2141 (2007). · Zbl 1140.15009
[15] Wunsch (J.), Zworski (M.).— The FBI transform on compact \(C^∞\) manifolds, Trans. A.M.S., 353(3), p. 1151-1167 (2001). · Zbl 0974.35005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.