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A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph

A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph The Sturm–Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from the part of the spectrum. A constructive method is developed for the solution of this problem, based on the Riesz-basicity of some sequence of vector functions. The local solvability of the inverse problem and the stability of its solution are proved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph

Analysis and Mathematical Physics , Volume 8 (1) – Apr 24, 2017

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-017-0172-x
Publisher site
See Article on Publisher Site

Abstract

The Sturm–Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from the part of the spectrum. A constructive method is developed for the solution of this problem, based on the Riesz-basicity of some sequence of vector functions. The local solvability of the inverse problem and the stability of its solution are proved.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Apr 24, 2017

References