Isomorphic Inverse Problems

Consider two inverse problems for Sturm–Liouville problems on the unit interval. This means that there are two corresponding mappings from a Hilbert space of potentials into their spectral data. They are called isomorphic if is a composition of and some isomorphism of onto itself. An isomorphic clas...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 32; no. 2; pp. 314 - 340
Main Author Korotyaev, E.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.06.2025
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Boundary conditions
Hilbert space
Inverse problems
Isomorphism
Mathematical and Computational Physics
Nonlinear analysis
Physics
Physics and Astronomy
Sturm-Liouville theory
Theoretical
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Summary:Consider two inverse problems for Sturm–Liouville problems on the unit interval. This means that there are two corresponding mappings from a Hilbert space of potentials into their spectral data. They are called isomorphic if is a composition of and some isomorphism of onto itself. An isomorphic class is a collection of inverse problems isomorphic to each other. We consider basic Sturm–Liouville problems on the unit interval and on the circle and describe their isomorphic classes of inverse problems. For example, we prove that the inverse problems for the case of Dirichlet and Neumann boundary conditions are isomorphic. The proof is based on nonlinear analysis. DOI 10.1134/S1061920824601745
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920824601745