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arxiv: 1207.4273 · v1 · pith:O5JK5KSMnew · submitted 2012-07-18 · 🧮 math.SP · math-ph· math.CV· math.MP

Asymptotic number of scattering resonances for generic Schrodinger operators

classification 🧮 math.SP math-phmath.CVmath.MP
keywords deltagenericnumberresonancesschrodingeractingapproximativelyasymptotic
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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.

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