Inverse Sturm-Liouville problems for non-Borg conditions

被引：2

作者：

Korotyaev, Evgeny L. ^{[1
]}

机构：

[1] St Petersburg State Univ, Dept Math Anal, Univ Skaya Nab 7-9, St Petersburg 199034, Russia

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2019年 / 27卷 / 03期

关键词：

Eigenvalues; Sturm-Liouville problem; PERIODIC POTENTIALS; SPECTRAL PROBLEM; HILL OPERATOR; IMPEDANCE; TERMS;

D O I：

10.1515/jiip-2018-0110

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Sturm-Liouville problems on the finite interval with non-Borg conditions. Using eigenvalues of four Sturm-Liouville problems, we construct the spectral data and show that the mapping from potential to spectral data is a bijection. Moreover, we obtain estimates of spectral data in terms of potentials.

引用

页码：445 / 452

页数：8

共 22 条

[1] *EINE UMKEHRUNG DER STURM-LIOUVILLESCHEN EIGENWERTAUFGABE - BESTIMMUNG DER DIFFERENTIALGLEICHUNG DURCH DIE EIGENWERTE [J].

BORG, G .

ACTA MATHEMATICA, 1946, 78 (01) :1-96

[2] SOLUTION OF THE INVERSE SPECTRAL PROBLEM FOR AN IMPEDANCE WITH INTEGRABLE DERIVATIVE .2. [J].

COLEMAN, CF ;

MCLAUGHLIN, JR .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1993, 46 (02) :185-212

[3]

COLEMAN CF, 1993, COMMUN PUR APPL MATH, V46, P145, DOI 10.1002/cpa.3160460203

[4] THE INVERSE STURM-LIOUVILLE PROBLEM .3. [J].

DAHLBERG, BEJ ;

TRUBOWITZ, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (02) :255-267

[5] GAPS AND BANDS OF ONE DIMENSIONAL PERIODIC SCHRODINGER-OPERATORS [J].

GARNETT, J ;

TRUBOWITZ, E .

COMMENTARII MATHEMATICI HELVETICI, 1984, 59 (02) :258-312

[6]

Hryniv R. O., 2004, FUNCTIONAL ANAL ITS, V197, P97, DOI DOI 10.1016/S0304-0208(04)80159-2.MR2098874

[7] THE INVERSE STURM-LIOUVILLE PROBLEM .2. [J].

ISAACSON, EL ;

MCKEAN, HP ;

TRUBOWITZ, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (01) :1-11

[8] THE INVERSE STURM-LIOUVILLE PROBLEM .1. [J].

ISAACSON, EL ;

TRUBOWITZ, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (06) :767-783

[9] The inverse problem for the Hill operator, a direct approach [J].

Kargaev, P ;

Korotyaev, E .

INVENTIONES MATHEMATICAE, 1997, 129 (03) :567-593

[10]

Korotyaev E, 2003, INT MATH RES NOTICES, V2003, P2019

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