2002
DOI: 10.1090/s0002-9939-02-06297-4
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$L^1$ convergence of the reconstruction formula for the potential function

Abstract: 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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Cited by 38 publications
(11 citation statements)
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“…Let Σ 1 ⊂ Σ be the subspace of all asymptotically equivalent nodal sequences and let Σ * 2 , then the corresponding function F n converges to q in L 1 (0, 1) as well as pointwisely a.e. It would be interesting to know whether the space Σ 1 can be expanded to include all sequences that converge to q in some way, which seems to be a more natural space.…”
Section: Introductionmentioning
confidence: 99%
“…Let Σ 1 ⊂ Σ be the subspace of all asymptotically equivalent nodal sequences and let Σ * 2 , then the corresponding function F n converges to q in L 1 (0, 1) as well as pointwisely a.e. It would be interesting to know whether the space Σ 1 can be expanded to include all sequences that converge to q in some way, which seems to be a more natural space.…”
Section: Introductionmentioning
confidence: 99%
“…This issue is well studied now and called the inverse nodal problem (cf. [9,10,16,24,27,35,41] etc.). For the problem (1.5), we have the following Theorem 1.3 (Uniqueness).…”
Section: Introductionmentioning
confidence: 99%
“…Later on, some remarkable results were obtained by some authors. For example, Chen, Law, Koyunbakan, Pinasco, etc have reconstructed the potential function and its derivatives from nodal points (zeros of eigenfunctions) in previous studies . In addition to the above, inverse nodal problem was extensively studied for some different problems in other studies .…”
Section: Introductionmentioning
confidence: 99%