Benedicte Alziary, Peter Takac
Abstract:
We investigate the compactness of the resolvent
of the Schrodinger operator
acting on the Banach space
,
, where
denotes
the ground state for
acting on
.
The potential
, bounded from below,
is a "relatively small" perturbation of a radially symmetric potential
which is assumed to be monotone increasing
(in the radial variable) and growing somewhat faster than
as
.
If
is the ground state energy for
,
i.e.
,
we show that the operator
is not only bounded, but also compact for
.
In particular, the spectra of
in
and
coincide; each eigenfunction of
belongs to
,
i.e., its absolute value is bounded by
.
Published May 15, 2007.
Math Subject Classifications: 47A10, 35J10, 35P15, 81Q15.
Key Words: Ground-state space; compact resolvent; Schrodinger operator;
monotone radial potential; maximum and anti-maximum principle;
comparison of ground states; asymptotic equivalence.
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Bénédicte Alziary CEREMATH - UMR MIP Université Toulouse 1 (Sciences Sociales) 21 Allées de Brienne, F-31000 Toulouse Cedex, France email: alziary@univ-tlse1.fr | |
Peter Takác Institut für Mathematik, Universität Rostock Universitätsplatz 1, D-18055 Rostock, Germany email: peter.takac@uni-rostock.de |
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