Inverse spectral problems for Sturm-Liouville operators with singular potentials, II. Reconstruction by two spectra
By Rostyslav Hryniv, Y. Mykytyuk. 2003
56 citations recorded by the source corpus.
We solve the inverse spectral problem of recovering the singular potentials $q\in W^{-1}_{2}(0,1)$ 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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e2523374fd1422778e63c23e0190de4cbf3334bd
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials (2006, background): “Namely, we proved in [ 16 ] that, as soon as the numbers λ 2 and � 2 are real, strictly increase with n, interlace, and obey (1.5) with l2-sequences ( en) and (e � n), then there exists a unique real-valued σ ∈ L2(0,1) such that {λ 2 } and {� 2 } are spectra of the Sturm–Liouville operators Tσ,D and”
- On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces (2006, unknown): “The paper [12] did not explicitly contain the dependence of C on σ, but, analyzing the proofs (see also [ 9 ] and [11]), we can easily see that C< e πR . Then, for ν =I mρ, the integral summand in (2.14) can”
- Transformation Operators for Sturm-Liouville Operators with Singular Potentials (2004, unknown): “Z x 0 j j n : Di erentiating recurrentrelations(3.5),we nd that (3.7) U 0n(x)= AUn(x)+ (x)JUn 1(x); and hence,with C1 := C(2jAj2 + 3)1=2, kUnkW 1 2 (M 2) := Z 1 0 jU 0nj 2 + jUnj 2 1=2 C1 (n 1)!”