Abstract
For the Schrödinger operator on the half line with real
compactly supported potential we show that:
Assume that we perturb a sequence of resonances and eigenvalues by a
sequence
from some Hilbert space. Then the new sequence is the sequence of
zeroes of the Jost function
for some unique real compactly supported potential, i.e.
it is a sequence of resonances and eigenvalues for this new potential.
Moreover, we
show that the measure associated with the zeros of the Jost
function is a Carleson measure. Using this fact we obtain a priori
estimates of resonances in terms of the Jost function.
This result will be published in Int. Math. Res. Notice.
Contact person:Erik Skibsted.