arXiv subjects

Christian Remling

Publications and source records attributed to Christian Remling.

21 records · Page 2Linked to original sources

arXiv2006

Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators

I present an example of a discrete Schr"odinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously identified borderline situation.

math.SP↗

arXiv2006

Finite propagation speed and kernel estimates for Schrödinger operators

I point out finite propagation speed phenomena for discrete and continuous Schrödinger operators and discuss kernel estimates from this point of view.

math-ph↗

arXiv2004

Schrödinger Operators with Many Bound States

Consider the Schrödinger operators $H_{\pm}=-d^2/dx^2\pm V(x)$. We present a method for estimating the potential in terms of the negative eigenvalues of these operators. Among the applications are inverse Lieb-Thirring inequalities and several sharp results concerning the spectral properties of $H_{\pm}$.

math-ph↗