14,837 research outputs found
Inverse spectral problems for energy-dependent Sturm-Liouville equations
We study the inverse spectral problem of reconstructing energy-dependent
Sturm-Liouville equations from their Dirichlet spectra and sequences of the
norming constants. For the class of problems under consideration, we give a
complete description of the corresponding spectral data, suggest a
reconstruction algorithm, and establish uniqueness of reconstruction. The
approach is based on connection between spectral problems for energy-dependent
Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page
Length spectra and degeneration of flat metrics
In this paper we consider flat metrics (semi-translation structures) on
surfaces of finite type. There are two main results. The first is a complete
description of when a set of simple closed curves is spectrally rigid, that is,
when the length vector determines a metric among the class of flat metrics.
Secondly, we give an embedding into the space of geodesic currents and use this
to get a boundary for the space of flat metrics. The geometric interpretation
is that flat metrics degenerate to "mixed structures" on the surface: part flat
metric and part measured foliation.Comment: 36 page
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