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Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data

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Abstract

The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.

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Authors and Affiliations

  1. Department of Mathematics, Saratov University, Saratov, Russia Astrakhanskaya 83, 410012, Saratov, Russia

    Mikhail Yu. Ignatiev

  2. Department of Mathematics, Tamkang University, Taipei, Taiwan, ROC

    Chung-Tsun Shieh

Authors
  1. Mikhail Yu. Ignatiev
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  2. Chung-Tsun Shieh
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Corresponding author

Correspondence to Mikhail Yu. Ignatiev.

Additional information

This research was supported in part by Grants 07-01-00003 and 07-01-92000-NSC-a of Russian Foundation for Basic Research and Taiwan National Science Council.

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Ignatiev, M.Y., Shieh, CT. Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data. Results. Math. 57, 183–194 (2010). https://doi.org/10.1007/s00025-009-0016-6

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  • DOI: https://doi.org/10.1007/s00025-009-0016-6

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