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1. CJM 2001 (vol 53 pp. 756)
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Correction to: Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions 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 $|V|$.
Categories:47A10, 47A40, 81U05 |
2. CJM 1998 (vol 50 pp. 538)
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Upper bounds for the resonance counting function of Schrödinger operators in odd dimensions 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.
Categories:47A10, 47A40, 81U05 |