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Asymptotic number of scattering resonances for generic Schrodinger operators

Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d>2 odd. Here V is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a. We show for generic potentials V that the number of resonances of -Delta+V with modulus less than r is approximatively equal to a constant times a^dr^d.

preprint2012arXivOpen access
Tien-Cuong DinhDuc-Viet Vu
math.CVmath-phmath.MPmath.SP
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Tien-Cuong DinhDuc-Viet Vu

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