2000
DOI: 10.1007/bf02355453
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Inverse problems of spectral analysis for differential operators and their applications

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Cited by 58 publications
(65 citation statements)
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“…Section 2 contains some preliminary results about the discrete eigenvalue problem (3)-(4) and the proof of the uniqueness result, Theorem 1.3. We also refer to [13] for the more general case of Jacobi operators. We note that our proof, unlike the proof of the corresponding continuous result, Theorem 1.1, follows neither the methods of Marčenkov [12] (who uses Parseval's equality) nor Levinson [10] (who uses the contour integral method) but is based on a matrix method that is taylored specifically to the discrete case.…”
Section: Theorem 12 (See [4 Theorem 143])mentioning
confidence: 99%
“…Section 2 contains some preliminary results about the discrete eigenvalue problem (3)-(4) and the proof of the uniqueness result, Theorem 1.3. We also refer to [13] for the more general case of Jacobi operators. We note that our proof, unlike the proof of the corresponding continuous result, Theorem 1.1, follows neither the methods of Marčenkov [12] (who uses Parseval's equality) nor Levinson [10] (who uses the contour integral method) but is based on a matrix method that is taylored specifically to the discrete case.…”
Section: Theorem 12 (See [4 Theorem 143])mentioning
confidence: 99%
“…Substituting (22) into (21) and using (17) we arrive at (19). Substituting (22) into (21) and using (17) we arrive at (19).…”
Section: ) For Each Sector S With Property (16) the Functions Ementioning
confidence: 99%
“…where ρ 0 n0 and ξ 1 are calculated by (14) and 18, respectively. Fix i = 1, r. There exists N 0 such that for all n > N 0 the function S i (x, λ n ) has exactly n (simple) zeros inside the interval (0, 1), namely:…”
Section: Inverse Nodal Problemsmentioning
confidence: 99%
“…Inverse nodal problems for Sturm-Liouville operators on an interval have been studied fairly completely in [1][6] and other papers. The main results on inverse spectral problems on an interval are presented in the monographs [7][14].…”
Section: Introductionmentioning
confidence: 99%