Non-selfadjoint matrix Sturm-Liouville operators with eigenvalue-dependent boundary conditions

Authors : Murat OLGUN

Pages : 607-614

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Publication Date : 2015-06-01

Article Type : Research Paper

Abstract :In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm-Liouville operator L generated in L 2 insert ignore into journalissuearticles values(R+, S); by the differential expression ` insert ignore into journalissuearticles values(y); = −y 00 + Q insert ignore into journalissuearticles values(x); y , x ∈ R+ : [0, ∞);, and the boundary condition y0insert ignore into journalissuearticles values(0); − β0 + β1λ + β2λ 2
y insert ignore into journalissuearticles values(0); = 0 where Q is a non-selfadjoint matrix valued function. Also using the uniqueness theorem of analytic functions we prove that L has a finite number of eigenvalues and spectral singularities with finite multiplicities
Keywords : Eigenvalues, Spectral Singularities, Spectral Analysis, Sturm Liouville Operator, Non Selfadjoint Matrix Operator