Semiclassical spectral instability of non-self-adjoint operators. II. (Instabilité spectrale semiclassique d’opérateurs non-autoadjoints. II.) (French) Zbl 1115.81032

Hager, Mildred

Ann. Henri Poincaré 7, No. 6, 1035-1064 (2006).

Summary: In this work, we consider analytic (pseudo-)differential operators as well as random perturbations. We show for the perturbed operators that with probability almost 1, the eigenvalues inside a subdomain of the pseudospectrum are distributed according to a bidimensional Weyl law.
[For Part I see the review above: the author, Ann. Fac. Sci. Toulouse, Math. (6) 15, No. 2, 243–280 (2006; Zbl 1114.81042).]

MSC:

81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis
35P20	Asymptotic distributions of eigenvalues in context of PDEs
47B25	Linear symmetric and selfadjoint operators (unbounded)
35R60	PDEs with randomness, stochastic partial differential equations
47G30	Pseudodifferential operators

Citations:

Zbl 1114.81042