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

Year 2015, Volume: 44 Issue: 3, 607 - 614, 01.06.2015

Murat Olgun

Abstract

In this paper we investigate discrete spectrum of the non-selfadjoint
matrix Sturm-Liouville operator L generated in L
2
(R+, S) by the differential expression
` (y) = −y
00 + Q (x) y , x ∈ R+ : [0, ∞),
and the boundary condition y0(0) −

β0 + β1λ + β2λ
2


y (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

References

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