Critical higher order Sturm–Liouville difference operators

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.

Keywords:

• Sturm–Liouville difference operator
• linear Hamiltonian difference system
• recessive system of solutions
• p-critical operator
• sub/supercritical operator

2000 Mathematics Subject Classification::

• 39A10
• 47B36
• 47B25

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]

Additional information

Notes on contributors

Petr Hasil

1