We provide a comprehensive analysis of matrix–valued Herglotz functions and illustrate
their applications in the spectral theory of self–adjoint Hamiltonian systems including matrix …

Using control of the growth of the transfer matrices, wediscuss the spectral analysis of
continuum and discrete half-line Schrödinger operators with slowly decaying potentials …

We investigate one-dimensional Schrödinger operators with asymptotically small potentials.
It will follow from our results that if with, then is an essential support of the absolutely …

For operators with homogeneous disorder, it is generally expected that there is a relation
between the spectral characteristics of a random operator in the infinite setup and the …

OPERATORS WITH SINGULAR CONTINUOUS SPECTRUM, V. SPARSE POTENTIALS §1.
Introduction This is one of a series of papers (see [2,11 Page 1 PROCEEDINGS OF THE …

We introduce the concept of a spectral shift operator and use it to derive Krein's spectral shift
function for pairs of self-adjoint operators. Our principal tools are operator-valued Herglotz …

We prove that one-dimensional reflectionless Schrödinger operators with spectrum a
homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and …

We study the model operator DA=(d/dt)+ A in L 2 (R; H) associated with the operator path A
(t) t=−∞∞, where (A f)(t)= A (t) f (t) for ae t∈ R, and appropriate f∈ L 2 (R; H)(with H a …

Localization at all energies is proved for the one-dimensional random Schrôdinger operator
with Poisson potential f (x-Xj (w)). The single site potential f is assumed to be non-negative …

Palle Jorgensen Steen Pedersen Feng Tian Applications and Their Harmonic Analysis Page 1
Lecture Notes in Mathematics 2160 Palle Jorgensen Steen Pedersen Feng Tian Extensions of …