The characteristic function for Jacobi matrices with applications

@article{Stampach2013TheCF,
  title={The characteristic function for Jacobi matrices with applications},
  author={F. Stampach and P. {\vS}ťov{\'i}{\vc}ek},
  journal={Linear Algebra and its Applications},
  year={2013},
  volume={438},
  pages={4130-4155}
}
  • F. Stampach, P. Šťovíček
  • Published 2013
  • Mathematics
  • Linear Algebra and its Applications
  • Abstract We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable domain, and show that its zero set actually coincides with the set of eigenvalues of J in that domain. As an application we construct several examples of Jacobi matrices for which the characteristic function can be expressed in terms of special functions… CONTINUE READING

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