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2013 Estimates of large eigenvalues and trace formula for the vectorial Sturm-Liouville equations
Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang
Rocky Mountain J. Math. 43(6): 2049-2078 (2013). DOI: 10.1216/RMJ-2013-43-6-2049

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.

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Chuan-Fu Yang. Zhen-You Huang. Xiao-Ping Yang. "Estimates of large eigenvalues and trace formula for the vectorial Sturm-Liouville equations." Rocky Mountain J. Math. 43 (6) 2049 - 2078, 2013. https://doi.org/10.1216/RMJ-2013-43-6-2049

Information

Published: 2013
First available in Project Euclid: 25 February 2014

zbMATH: 1292.34082
MathSciNet: MR3178456
Digital Object Identifier: 10.1216/RMJ-2013-43-6-2049

Subjects:
Primary: 34B24, 34L20

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

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Vol.43 • No. 6 • 2013
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