On an Inverse Transmission Problem From Complex Eigenvalues

被引：17

作者：

Buterin, S. A. ^{[1
]}

Yang, C. -F. ^{[2
]}

机构：

[1] Saratov Univ, Dept Math, Astrakhanskaya 83, Saratov 410012, Russia

[2] Nanjing Univ Sci & Technol, Dept Appl Math, Nanjing 210094, Jiangsu, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2017年 / 71卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

Inverse spectral problem; transmission eigenvalue problem; complex transmission eigenvalues; SPECTRAL PROBLEM; OPERATOR;

D O I：

10.1007/s00025-015-0512-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that for unique determination of q(x) in the boundary value problem - y '' + q(x)y = lambda y, y(0) = 0, y(1) cos root lambda a = y'(1) sin root lambda a/root lambda for a > 1 it is sufficient to specify only a part of the spectrum with exception of infinitely many eigenvalues having the asymptotics lambda (k,1) = (a-1)(-2) pi(2) k (2) + O(1), k >= 1, and forming McLaughlin-Polyakov's almost real infinite subspectrum (McLaughlin and Polyakov in J Differ Equ 107:351-382, 1994). This result improves the uniqueness theorem in Aktosun et al. (Inverse Probl 27:115004, 2011).

引用

页码：859 / 866

页数：8

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