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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$L^1$ convergence of the reconstruction formula for the potential function


Authors: Ya-Ting Chen, Y. H. Cheng, C. K. Law and J. Tsay
Journal: Proc. Amer. Math. Soc. 130 (2002), 2319-2324
MSC (2000): Primary 34A55; Secondary 34B24
Published electronically: January 17, 2002
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Abstract: It is known that the potential function of the Sturm-Liouville problem can be reconstructed from the nodal data by a pointwise limit. We show that this convergence is in fact $L^1$.


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Ya-Ting Chen
Affiliation: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China
Email: chenyt@math.nsysu.edu.tw

Y. H. Cheng
Affiliation: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China
Email: jengyh@math.nsysu.edu.tw

C. K. Law
Affiliation: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China
Email: law@math.nsysu.edu.tw

J. Tsay
Affiliation: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424, Republic of China
Email: tsay@math.nsysu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06297-4
PII: S 0002-9939(02)06297-4
Keywords: Inverse nodal problem, potential function, reconstruction formula
Received by editor(s): November 21, 2000
Received by editor(s) in revised form: February 20, 2001
Published electronically: January 17, 2002
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society