New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
 Mémoires de la Société Mathématique de France 2014; 144 pp; softcover Number: 136 ISBN-10: 2-85629-780-3 ISBN-13: 978-2-85629-780-3 List Price: US$52 Member Price: US$41.60 Order Code: SMFMEM/136 The author considers semi-classical Schrödinger operators with potentials supported in a bounded strictly convex subset $$\mathcal{O}$$ of $$\mathbb{R}^n$$ with smooth boundary. Letting $$h$$ denote the semi-classical parameter, the author considers classes of small random perturbations and shows that with probability very close to 1, the number of resonances in rectangles $$[a,b]-i[0,ch^{\frac 23}$$] is equal to the number of eigenvalues in $$[a,b]$$ of the Dirichlet realization of the unperturbed operator in $$\mathcal{O}$$ up to a small remainder. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians. Table of Contents Introduction The result Some elements of the proof Grushin problems and determinants Complex dilations Semi-classical Sobolev spaces Reductions to $$\mathcal{O}$$ and to $$\partial\mathcal{O}$$ Some ODE preparations Parametrix for the exterior Dirichlet problem Exterior Poisson operator and DN map The interior DN map Some determinants Upper bounds on the basic determinant Some estimates for $$P_\mathrm{out}$$ Perturbation matrices and their singular values End of the construction End of the proof of Theorem 2.2 and proof of Proposition 2.4 Appendix. WKB estimates on an interval Bibliography