J. London Math. Soc. (2) 88, 801-828 (2013).
Inverse Spectral Theory for Sturm-Liouville Operators with Distributional Potentials
We discuss inverse spectral theory for singular differential operators on arbitrary intervals
(a,b) ⊆ ℝ
associated with rather general differential expressions of the type
τ f = 1/r ( - (p[f' + s f])' + s p[f' + s f] + qf),
where the coefficients p
are Lebesgue measurable on (a,b)
, s ∈ L1loc((a,b); dx)
and real-valued with p\not=0
. In particular, we explicitly permit certain distributional potential coefficients.
The inverse spectral theory results derived in this paper include those implied by the spectral measure,
by two-spectra and three-spectra, as well as local Borg-Marchenko-type inverse spectral results. The
special cases of Schrödinger operators with distributional potentials and Sturm-Liouville operators
in impedance form are isolated, in particular.
MSC2010: Primary 34B24, 34L05; Secondary 34L40, 46E22.
Keywords: Sturm-Liouville operators, distributional coefficients, inverse spectral theory.