Harmonic Functions of Polynomial Growth on Certain Complete Manifolds.
Resonances for Schrödinger operators with compactly supported potentials
We describe the generic behavior of the resonance counting function for a Schrödinger operator with a bounded, compactly-supported real or complex valued potential in dimensions. This note contains a sketch of the proof of our main results [, ] that generically the order of growth of the resonance counting function is the maximal value in the odd dimensional case, and that it is the maximal value on each nonphysical sheet of the logarithmic Riemann surface in the even dimensional case. We...
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