A vectorial inverse nodal problem |
| |
Authors: | Yan-Hsiou Cheng Chung-Tsun Shieh C. K. Law |
| |
Affiliation: | Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, Republic of China ; Department of Mathematics, Tamkang University, Tamsui, Taipei County, Taiwan 251, Republic of China ; Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, Republic of China |
| |
Abstract: | Consider the vectorial Sturm-Liouville problem: where is a continuous symmetric matrix-valued function defined on , and and are real symmetric matrices. An eigenfunction of the above problem is said to be of type (CZ) if any isolated zero of its component is a nodal point of . We show that when , there are infinitely many eigenfunctions of type (CZ) if and only if are simultaneously diagonalizable. This indicates that can be reconstructed when all except a finite number of eigenfunctions are of type (CZ). The results supplement a theorem proved by Shen-Shieh (the second author) for Dirichlet boundary conditions. The proof depends on an eigenvalue estimate, which seems to be of independent interest. |
| |
Keywords: | |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Proceedings of the American Mathematical Society》下载全文 |
|