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Dispersive Estimates for Schrödinger Operators in Dimension Two

✍ Scribed by W. Schlag

Publisher: Springer
Year: 2005
Tongue: English
Weight: 319 KB
Volume: 257
Category: Article
ISSN: 0010-3616
DOI: 10.1007/s00220-004-1262-9

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Using a probabilistic approach based on the Feynman-Kac formalism and the spectral radius of the shuttle operator, we prove that two-dimensional Schrödinger operators \(H=-\Delta+V\) with short-range potentials \(V\) satisfying \(V(x)=\left.\right|_{\mid x \rightarrow \infty} 0\left(|x|^{-2}(\ln (|x