Reconstruction of the solution of inverse Sturm–Liouville problem
Abstract In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on [ 0 , 1 / 2 ] $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01860-4 |
| Summary: | Abstract In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on [ 0 , 1 / 2 ] $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue. |
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| ISSN: | 1687-2770 |