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Asymptotic distribution of resonances for convex obstacles. (English) Zbl 0989.35099
The paper deals with the subject of locating and estimating resonances for convex bodies. It continues authors’ previous work on upper bounds on the number of resonances in neighbourhoods of the real axis. The authors turn resonances into eigenvalues of a nonselfadjoint operator, proceed to a second microlocal reduction of the scaled problem to the boundary and establish a trace formula for the reduced problem.

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35J10 Schrödinger operator, Schrödinger equation
35P25 Scattering theory for PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
58J37 Perturbations of PDEs on manifolds; asymptotics
81U05 \(2\)-body potential quantum scattering theory
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