Besov spaces for Schrodinger operators with barrier potentials

Details Besov spaces for Schrodinger operators with barrier potentials Besov spaces for Schrodinger operators with barrier potentials

2004-11-16

arxiv.org/abs/math/0411348v1

Mathematics

Classical Analysis and ODEs

35 pages

Scientific paper

Let H be a Schrodinger operator with barrier potential on the real line. We define the Besov spaces for H by developing the associated Littlewood-Paley theory. This theory depends on the decay estimates of the spectral operator in the high and low energies. We also prove a Mikhlin-Hormander type multiplier theorem on these spaces, including the Lp boundedness result. Our approach has potential applications to other Schrodinger operators with short-range potentials, as well as in higher dimensions.

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