Itô diffusions, modified capacity and harmonic measure. Applications to Schrödinger operators.
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en
Article de revue
Este ítem está publicado en
International Mathematics Research Notices. 2012, vol. 14, p. 3127-3181
Oxford University Press (OUP)
Resumen en inglés
We observe that some special Itô diffusions are related to scattering properties of a Schrödinger operator on R^d, d>1. We introduce Feynman-Kac type formulae for these stochastic processes which lead us to results on the ...Leer más >
We observe that some special Itô diffusions are related to scattering properties of a Schrödinger operator on R^d, d>1. We introduce Feynman-Kac type formulae for these stochastic processes which lead us to results on the preservation of the a.c. spectrum of the Schrödinger operator. To better understand the analytic properties of the processes, we construct and study a special version of the potential theory. The modified capacity and harmonic measure play an important role in these considerations. Various applications to Schrödinger operators are also given. For example, we relate the presence of the absolutely continuous spectrum to the geometric properties of the support of the potential.< Leer menos
Palabras clave en inglés
Absolutely continuous spectrum
Schrödinger operator
Itô stochastic calculus
Feynman-Kac type formulae
special potential theory
modified capacity
modified harmonic measure
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