- 02-394 Christian Remling
- Universal bounds on spectral measures of one-dimensional Schrödinger operators
Sep 23, 02
(auto. generated ps),
of related papers
Abstract. Consider a Schrödinger operator $H=-d^2/dx^2+V(x)$ on $L_2(0,\infty)$
and suppose that an initial piece of the potential $V(x)$, $0<x<N$ is
known. We show that this information leads to upper and lower bounds on
the spectral measure of intervals with a certain minimum length. This
length scale is set by the eigenvalues of the problems on $[0,N]$. So in
a sense (and perhaps somewhat surprisingly) the behavior of $V(x)$ becomes
less important if $x$ grows.
The results of this paper are developments of classical work of
Chebyshev and Markov on orthogonal polynomials.