Transfer functions and local spectral uniqueness for Sturm-Liouville operators, canonical systems and strings

DOI10.1007/s00020-016-2292-3zbMath1365.34033arXiv1604.00416OpenAlexW2337522494WikidataQ55670586 ScholiaQ55670586MaRDI QIDQ2629356

Heinz K. Langer

Publication date: 6 July 2016

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00416

zbMATH Keywords

transfer functioncanonical systemsinverse problemsspectral measureSturm-Liouville operatorsstringslocal spectral uniquenessMarchenko-Borg theorem

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Weyl theory and its generalizations for ordinary differential equations (34B20) Inverse problems involving ordinary differential equations (34A55) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32) Local spectral properties of linear operators (47A11)

Related Items (6)

On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations ⋮ The local Borg–Marchenko uniqueness theorem of matrix‐valued Dirac‐type operators for coefficients locally smooth at the right endpoint ⋮ Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints ⋮ Directing Functionals and De Branges Space Completions in Almost Pontryagin Spaces ⋮ On the class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl-Titchmarsh theory ⋮ The local Borg-Marchenko uniqueness theorem for potentials locally smooth at the right endpoint

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