SCHRODINGER-OPERATORS - GEOMETRIC ESTIMATES IN TERMS OF THE OCCUPATION TIME

Authors
DEMUTH M KIRSCH W MCGILLIVRAY I
Citation
M. Demuth et al., SCHRODINGER-OPERATORS - GEOMETRIC ESTIMATES IN TERMS OF THE OCCUPATION TIME, Communications in partial differential equations, 20(1-2), 1995, pp. 37-57
Citations number
12
Categorie Soggetti
Mathematics,"Mathematics, Pure",Mathematics,Mathematics
Journal title
Communications in partial differential equations → ACNP
ISSN journal
03605302
Volume
20
Issue
1-2
Year of publication
1995
Pages
37 - 57
Database
ISI
SICI code
0360-5302(1995)20:1-2<37:S-GEIT>2.0.ZU;2-N
Abstract
The difference of Schrodinger and Dirichlet semigroups is expressed in terms of the Laplace transform of the Brownian motion occupation time . This implies quantitative upper and lower bounds for the operator no rms of the corresponding resolvent differences. One spectral theoretic al consequence is an estimate for the eigenfunction for a Schrodinger operator in a ball where the potential is given as a cone indicates fu nction.