Half-Inverse spectral problems for Sturm-Liouville operators with singular potentials

被引：81
作者：
Hryniv, RO
Mykytyuk, YV
机构：
[1] Inst Appl Problems Mech & Math, UA-79601 Lvov, Ukraine
[2] Lviv Natl Univ, UA-79602 Lvov, Ukraine
来源：
INVERSE PROBLEMS | 2004年 / 20卷 / 05期
关键词：
D O I：
10.1088/0266-5611/20/5/006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The half-inverse spectral problem for a Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. We give the necessary and sufficient conditions for solvability of the half-inverse spectral problem for the class of Sturm-Liouville operators with singular potentials from the space W-2(-1)(0,1) and provide a reconstruction algorithm.
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页码：1423 / 1444
页数：22
相关论文
共 31 条
[1]   INVERSE EIGENVALUE PROBLEMS WITH DISCONTINUOUS COEFFICIENTS [J].
ANDERSSON, LE .
INVERSE PROBLEMS, 1988, 4 (02) :353-397
[2]   INVERSE EIGENVALUE PROBLEMS FOR A STURM-LIOUVILLE EQUATION IN IMPEDANCE FORM [J].
ANDERSSON, LE .
INVERSE PROBLEMS, 1988, 4 (04) :929-971
[3]  
[Anonymous], AM MATH SOC TRANSL M
[4]   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
[5]  
COLEMAN CF, 1993, COMMUN PUR APPL MATH, V46, P145, DOI 10.1002/cpa.3160460203
[6]   Inverse spectral analysis with partial information on the potential .3. Updating boundary conditions [J].
delRio, R ;
Gesztesy, F ;
Simon, B .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 1997, 1997 (15) :751-758
[7]  
DELRIO R, 1990, SIAM J APPL MATH, V50, P1745
[8]   Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum [J].
Gesztesy, F ;
Simon, B .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (06) :2765-2787
[9]  
GOHBERG I, 1969, AM MATH SOC TRANSL M, V18
[10]  
GOHBERG I, 1967, THEORY VOLTERRA OPER
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