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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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.

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

First available in Project Euclid: 25 February 2014

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

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


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.

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