The purpose of this note is to provide a simple proof of the sharp polynomial upper bound for the resonance counting function of a Schr\"odinger operator in odd dimensions. At the same time we generalize the result to the class of super-exponentially decreasing potentials.

MSC Classifications:

47A10, 47A40, 81U05 show english descriptions Spectrum, resolvent
Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
$2$-body potential scattering theory [See also 34E20 for WKB methods] 47A10 - Spectrum, resolvent
47A40 - Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
81U05 - $2$-body potential scattering theory [See also 34E20 for WKB methods]

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