A dispersive bound for three-dimensional Schroedinger operators with zero energy eigenvalues
Year: 2008
Type: preprint
Abstract: We prove a dispersive estimate for the evolution of Schroedinger operators $H = -Δ+ V(x)$ in ${\mathbb R}^3$. The potential is allowed to be a complex-valued function belonging to $L^p(\R^3)\cap L^q(\R^3)$, $p < \frac32 < q$, so that $H$ need not be self-adjoint or even symmetric. Some additional spectral conditions are imposed, namely that no resonances of $H$ exist anywhere within the interval $[0,\infty)$ and that eigenfunctions at zero (including generalized eigenfunctions) decay rapidly enough to be integrable.
Source: arXiv (Cornell University)
Author: Goldberg, Michael
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2074881275