Ito diffusions, modified capacity and harmonic measure. Applications to Schrodinger operators

Details Ito diffusions, modified capacity and harmonic measure. Applications to Schrodinger operators Ito diffusions, modified capacity and harmonic measure. Applications to Schrodinger operators

2010-12-17

arxiv.org/abs/1012.3785v1

Mathematics

Analysis of PDEs

Scientific paper

Using certain Ito's equation, we introduce the probability on the space of
paths and show its relevance to the scattering properties of multidimensional
Schrodinger operator. To relate the geometry of the support of potential to the
spectral type we develop a special variant of Potential theory and prove some
estimates on the modified Harmonic measure.

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