Abstract
We investigate the so-called critical 2nth-order Sturm–Liouville difference operators and associated symmetric banded matrices. We show that arbitrarily small (in a certain sense) negative perturbation of a non-negative critical operator leads to an operator which is no longer non-negative.
Acknowledgement
This research is supported by the Grants 201/07/0145 and 201/09/J009 of the Czech Grant Agency of the Czech Republic and the Research Project MSM0022162409 of the Czech Ministry of Education.
Notes
1. Email: [email protected]