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- W2077884589 abstract "We prove that the resonance counting functions for Schrodinger operators H v = -Δ + V on L 2 (ℝ d ), for d ≥ 2 even, with generic, compactly-supported, real- or complex-valued potentials V, have the maximal order of growth d on each sheet Λ m , m ∈ ℤ {O}, of the logarithmic Riemann surface. We obtain this result by constructing, for each m ∈ ℤ {O}, a plurisubharmonic function from a scattering determinant whose zeros on the physical sheet Ao determine the poles on Λ m . We prove that the order of growth of the counting function is related to a suitable estimate on this function that we establish for generic potentials. We also show that for a potential that is the characteristic function of a ball, the resonance counting function is bounded below by C m r d on each sheet Λ m , m ∈ ℤ {0}." @default.
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- W2077884589 date "2010-01-01" @default.
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- W2077884589 title "Maximal order of growth for the resonance counting functions for generic potentials in even dimensions" @default.
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- W2077884589 doi "https://doi.org/10.1512/iumj.2010.59.4007" @default.
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