364 research outputs found
The Generalized Legendre transform and its applications to inverse spectral problems
Let be a Riemannian manifold, an isometric
action on of an -torus and a bounded
-invariant smooth function. By -invariance the Schr\"odinger operator,
, restricts to a self-adjoint operator on
, being a weight of and a large
positive integer. Let be the asymptotic support of the
spectrum of this operator. We will show that extend to a function,
and that, modulo assumptions on and
one can recover from , i.e. prove that is spectrally determined. The
main ingredient in the proof of this result is the existence of a "generalized
Legendre transform" mapping the graph of onto the graph of .Comment: 23 page
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