 0468 Kurt Broderix, Hajo Leschke, Peter Mueller
 Continuous integral kernels for unbounded Schroedinger semigroups and
their spectral projections
(325K, Postscript)
Mar 8, 04

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. By suitably extending a FeynmanKac formula of Simon
[Canadian Math. Soc. Conf. Proc. \textbf{28} (2000), 317321], we
study oneparameter semigroups generated by (the negative of) rather general Schr{\"o}dinger operators, which may be unbounded from below and include a magnetic vector potential. In particular, a common domain of essential selfadjointness for such a semigroup is specified. Moreover, each member of the semigroup is proven to be a maximal Carleman operator with a continuous integral kernel given by a Brownianbridge expectation. The results are used to show that the spectral projections of the generating Schr\"odinger operator also act as Carleman operators with continuous integral kernels. Applications to Schr{\"o}dinger operators with rather general random scalar potentials include a rigorous justification of an integralkernel representation of their integrated density of states  a relation frequently used in the physics literature on disordered solids.
 Files:
0468.src(
0468.comments ,
0468.keywords ,
jfa.ps )