Mixed data in inverse spectral problems for the Schrödinger operators

We consider the Schrödinger operator on a finite interval with an L^1 -potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and point masses of the spectral measure (or norming constants) corresponding to the first spectrum. We also solve...

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Bibliographic Details
Published inJournal of spectral theory Vol. 11; no. 1; pp. 281 - 322
Main Author Hatinoglu, Burak
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2021
Subjects
Boundary value problems
Functions, Inverse
Mathematical research
Schrodinger equation
United States
Online AccessGet full text
ISSN1664-039X
1664-0403
1664-0403
DOI10.4171/jst/341

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Summary:We consider the Schrödinger operator on a finite interval with an L^1 -potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and point masses of the spectral measure (or norming constants) corresponding to the first spectrum. We also solve this Borg–Marchenko-type problem under some conditions on two spectra, when missing part of the second spectrum and known point masses of the spectral measure have different index sets.
ISSN:1664-039X
1664-0403
1664-0403
DOI:10.4171/jst/341