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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Reconstructing potentials from zeros of one eigenfunction


Authors: Xinfu Chen, Y. H. Cheng and C. K. Law
Journal: Trans. Amer. Math. Soc. 363 (2011), 4831-4851
MSC (2010): Primary 34B24, 47A52; Secondary 34A55, 49M30
Published electronically: April 20, 2011
MathSciNet review: 2806693
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Abstract: We study an inverse nodal problem, concerning the reconstruction of a potential of a Sturm-Liouville operator, by using zeros of one eigenfunction as input. We propose three methods for the reconstruction, one of which is the Tikhonov regularization method. The explicit error bounds are calculated for all three methods. In case there is measurement error, the Tikhonov regularization method is still convergent. The study is motivated by physical considerations.


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Additional Information

Xinfu Chen
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: xinfu@pitt.edu

Y. H. Cheng
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
Email: jengyh@math.nsysu.edu.tw

C. K. Law
Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan – and – National Center for Theoretical Sciences, Taiwan
Email: law@math.nsysu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05258-X
PII: S 0002-9947(2011)05258-X
Keywords: Inverse nodal problem, Sturm-Liouville operators, Tikhonov regularization, error bound
Received by editor(s): November 4, 2008
Received by editor(s) in revised form: November 18, 2009
Published electronically: April 20, 2011
Article copyright: © Copyright 2011 American Mathematical Society