Spectral theory of difference operators with almost constant coefficients II

Abstract

We show that the operators whose coefficients are approximately constant in a general sense have an absolutely continuous spectrum which is equal to that of the corresponding constant coefficient operator. For such operators, the absolutely continuous spectrum can be read off from the associated characteristic polynomial. This generalizes the classical results on second-order operators and extends those of higher order differential operators to the difference setting. Our approach relies on an analysis of the associated difference equation with the help of uniform asymptotic summation techniques.

2000 Mathematics Subject Classification::

• Primary 39A20
• Secondary 47A55

Keywords:

• difference operators
• singular continuous spectrum
• absolutely continuous spectrum
• eigenvalues

Notes

1. [email protected]

Additional information

Notes on contributors

H. Behncke

1