# 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} }

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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