Jost solution and the spectral properties of the matrix-valued difference operators

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• 作者：Yelda Aygar ; ^{yaygar@science.ankara.edu.tr} ; Elgiz Bairamov ^{bairamov@science.ankara.edu.tr}
• 关键词：Difference equations ; Spectral analysis ; Eigenvalues ; Continuous spectrum ; Jost function
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 June, 2012
• 卷：218
• 期：19
• 页码：9676-9681
• 文件大小：175 K

摘要

In this paper, we find polynomial type Jost solution of the selfadjoint matrix-valued difference equation of second order. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem we prove that, the selfadjoint operator L generated by the matrix-valued difference expression of second order has the continuous spectrum filling the segment . We also study the eigenvalues of L and prove that it has a finite number of simple real eigenvalues.