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Correction to: Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions

  Published:2001-08-01
 Printed: Aug 2001
  • Richard Froese
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Abstract

The proof of Lemma~3.4 in [F] relies on the incorrect equality $\mu_j (AB) = \mu_j (BA)$ for singular values (for a counterexample, see [S, p.~4]). Thus, Theorem~3.1 as stated has not been proven. However, with minor changes, we can obtain a bound for the counting function in terms of the growth of the Fourier transform of $|V|$.
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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