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Spectral isomorphisms between generalized Sturm-Liouville problems. (English) Zbl 1038.34027

Gohberg, Israel (ed.) et al., Linear operators and matrices. The Peter Lancaster anniversary volume. Basel: Birkhäuser (ISBN 3-7643-6655-9/hbk). Oper. Theory, Adv. Appl. 130, 135-152 (2002).
The authors consider Sturm-Liouville differential equations on \([0, 1]\) with separated boundary conditions in 0 and 1, the latter being allowed to depend on the eigenvalue parameter linearly. They characterize all maps between such eigenvalue problems which preserve the spectrum and some norming constants (with an index shift 1). This leads to results on existence and uniqueness for the inverse spectral problem connected with such Sturm-Liouville problems.
For the entire collection see [Zbl 1005.00035].

MSC:

34B24 Sturm-Liouville theory
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
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