13 research outputs found
Inverse spectral problems for Sturm-Liouville operators with singular potentials, IV. Potentials in the Sobolev space scale
We solve the inverse spectral problems for the class of Sturm--Liouville
operators with singular real-valued potentials from the Sobolev space
W^{s-1}_2(0,1), s\in[0,1]. The potential is recovered from two spectra or from
the spectrum and norming constants. Necessary and sufficient conditions on the
spectral data to correspond to the potential in W^{s-1}_2(0,1) are established.Comment: 16 page
Inverse spectral problems for Sturm-Liouville operators with singular potentials, II. Reconstruction by two spectra
We solve the inverse spectral problem of recovering the singular potentials
of Sturm-Liouville operators by two spectra. The
reconstruction algorithm is presented and necessary and sufficient conditions
on two sequences to be spectral data for Sturm-Liouville operators under
consideration are given.Comment: 14 pgs, AmS-LaTex2
Inverse spectral problems for Dirac operators on a finite interval
We consider the direct and inverse spectral problems for Dirac operators that
are generated by the differential expressions \mathfrak t_q:=\frac{1}{i}[I&0
0&-I]\frac{d}{dx}+[0&q q^*&0] and some separated boundary conditions. Here
is an matrix-valued function with entries belonging to
and is the identity matrix. We give a
complete description of the spectral data (eigenvalues and suitably introduced
norming matrices) for the operators under consideration and suggest an
algorithm of reconstructing the potential from the corresponding spectral
data.Comment: 23 page
Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials
We give a complete description of the set of spectral data (eigenvalues and
specially introduced norming constants) for Sturm--Liouville operators on the
interval with matrix-valued potentials in the Sobolev space
and suggest an algorithm reconstructing the potential from the spectral data
that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO
Inverse spectral problems for Sturm-Liouville operators with singular potentials
The inverse spectral problem is solved for the class of Sturm-Liouville
operators with singular real-valued potentials from the space .
The potential is recovered via the eigenvalues and the corresponding norming
constants. The reconstruction algorithm is presented and its stability proved.
Also, the set of all possible spectral data is explicitly described and the
isospectral sets are characterized.Comment: Submitted to Inverse Problem