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Matrix Sturm-Liouville equation with a Bessel-type singularity on a finite interval

Authors
  • Bondarenko, Natalia
Type
Preprint
Publication Date
Feb 22, 2016
Submission Date
Feb 22, 2016
Identifiers
arXiv ID: 1602.06882
Source
arXiv
License
Yellow
External links

Abstract

The matrix Sturm-Liouville equation on a finite interval with a Bessel-type singularity in the end of the interval is studied. Special fundamental systems of solutions for this equation are constructed: analytic Bessel-type solutions with the prescribed behavior at the singular point and Birkhoff-type solutions with the known asymptotics for large values of the spectral parameter. The asymptotic formulas for Stokes multipliers, connecting these two fundamental systems of solutions, are derived. We also set boundary conditions and obtain asymptotic formulas for the spectral data (the eigenvalues and the weight matrices) of the boundary value problem. Our results will be useful in the theory of direct and inverse spectral problems.

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