Year: 2017
Type: article
Abstract: Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator -\Delta+V in L^2(\mathbb R^\nu) with complex potential has absolute value at most a constant times \|V\|_{\gamma+\nu/2}^{(\gamma+\nu/2)/\gamma} for 0<\gamma\leq\nu/2 in dimension \nu\geq 2 . We prove this conjecture for radial potentials if 0<\gamma<\nu/2 and we 'almost disprove' it for general potentials if 1/2<\gamma<\nu/2 . In addition, we prove various bounds that hold, in particular, for positive eigenvalues.
Source: Journal of Spectral Theory
DOI: 10.4171/jst/173
Authors: Rupert L. Frank, Barry Simon
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2255226340