A vectorial inverse nodal problem

Authors:
Yan-Hsiou Cheng, Chung-Tsun Shieh and C. K. Law

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1475-1484

MSC (2000):
Primary 34B24, 34C10

DOI:
https://doi.org/10.1090/S0002-9939-04-07679-8

Published electronically:
November 19, 2004

MathSciNet review:
2111948

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Yan-Hsiou Cheng**

Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, Republic of China

Email:
jengyh@math.nsysu.edu.tw

**Chung-Tsun Shieh**

Affiliation:
Department of Mathematics, Tamkang University, Tamsui, Taipei County, Taiwan 251, Republic of China

Email:
ctshieh@math.tku.edu.tw

**C. K. Law**

Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, Republic of China

Email:
law@math.nsysu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-04-07679-8

Received by editor(s):
August 27, 2003

Received by editor(s) in revised form:
February 4, 2004

Published electronically:
November 19, 2004

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.