Rocky Mountain Journal of Mathematics

Estimates of large eigenvalues and trace formula for the vectorial Sturm-Liouville equations

Chuan-Fu Yang, Zhen-You Huang, and Xiao-Ping Yang

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Abstract

This paper describes the $N$-dimensional vectorial Sturm-Liouville problem with coupled boundary conditions. We first derive the asymptotic expressions of large eigenvalues for the vectorial Sturm-Liouville operator with smooth coefficients. In addition, the regularized trace formula for the operator is calculated with residue techniques in complex analysis. These formulae are then used to obtain some results of inverse eigenvalue problems in the spirit of Ambarzumyan.

Article information

Source
Rocky Mountain J. Math., Volume 43, Number 6 (2013), 2049-2078.

Dates
First available in Project Euclid: 25 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1393336669

Digital Object Identifier
doi:10.1216/RMJ-2013-43-6-2049

Mathematical Reviews number (MathSciNet)
MR3178456

Zentralblatt MATH identifier
1292.34082

Subjects
Primary: 34B24: Sturm-Liouville theory [See also 34Lxx] 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions

Keywords
Vectorial Sturm-Liouville problem eigenvalue asymptotics trace formula inverse spectral problem

Citation

Yang, Chuan-Fu; Huang, Zhen-You; Yang, Xiao-Ping. Estimates of large eigenvalues and trace formula for the vectorial Sturm-Liouville equations. Rocky Mountain J. Math. 43 (2013), no. 6, 2049--2078. doi:10.1216/RMJ-2013-43-6-2049. https://projecteuclid.org/euclid.rmjm/1393336669


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