Inverse spectral problems for Sturm–Liouville operators with singular potentials
By Rostyslav Hryniv, Y. Mykytyuk. 2002
149 citations recorded by the source corpus.
The inverse spectral problem is solved for the class of Sturm–Liouville operators with singular real-valued potentials from the space W2−1 (0, 1). 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.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/cf730c5374a5c7df510a4db332db442534ff1e8d
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials (2006, unknown): “[26, Ch. 1.3] and [ 15 ]) that for f ∈ L2 the numbers ξn have the form ξn = πn 2 + ˜ ξn”
- On spectral theory for Schrödinger operators with strongly singular potentials (2005, background): “, [19], [48], [49], [50] and the references therein), while other groups study strongly singular interactions in the context of Pontryagin spaces (we refer, e.”
- Transformation Operators for Sturm-Liouville Operators with Singular Potentials (2004, unknown): “e repeat it m times among ξ2n−1 or ξ2n respectively. We shall order ξk so that Reξ2n+1 >Reξ2n−1 or Reξ2n+1 = Reξ2n−1 and Imξ2n+1 ≥ Imξ2n−1 and similarly for ξ2n. It is known (cf. [25, Ch. 1.3] and [15]) that for f∈ L2 the numbers ξn have the form ξn = πn 2 +ξ˜ n for some ℓ2-sequence (ξ˜n)n∈N (in ”