An inverse spectral problem for a star graph of Krein strings
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Jonathan Eckhardt
Abstract
We solve an inverse spectral problem for a star graph of Krein strings, where the known spectral data comprises the spectrum associated with the whole graph, the spectra associated with the individual edges as well as so-called coupling matrices. In particular, we show that these spectral quantities uniquely determine the weight within the class of Borel measures on the graph, which give rise to trace class resolvents. Furthermore, we obtain a concise characterization of all possible spectral data for this class of weights.
I gratefully acknowledge the kind hospitality of the Institut Mittag-Leffler (Djursholm, Sweden) during the scientific program on Inverse Problems and Applications in Spring 2013, where this article was written.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity
- Universal and homogeneous embeddings of dual polar spaces of rank 3 defined over quadratic alternative division algebras
- Mixing operators and small subsets of the circle
- Singularities on the base of a Fano type fibration
- Stable representation homology and Koszul duality
- An inverse spectral problem for a star graph of Krein strings
- Uniqueness of self-similar shrinkers with asymptotically cylindrical ends
- Ultraproducts, QWEP von Neumann algebras, and the Effros–Maréchal topology
Articles in the same Issue
- Frontmatter
- Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity
- Universal and homogeneous embeddings of dual polar spaces of rank 3 defined over quadratic alternative division algebras
- Mixing operators and small subsets of the circle
- Singularities on the base of a Fano type fibration
- Stable representation homology and Koszul duality
- An inverse spectral problem for a star graph of Krein strings
- Uniqueness of self-similar shrinkers with asymptotically cylindrical ends
- Ultraproducts, QWEP von Neumann algebras, and the Effros–Maréchal topology
