Display Abstract

Title Spectral Analysis of a $q$-Difference Operator

Name Martin Bohner
Country USA
Email bohner@mst.edu
Co-Author(s) M. Bekker, A. Herega, H. Voulov
Submit Time 2010-02-23 17:04:10
Special Session 48: Differential, Difference, and Dynamic Equations
For a number $q$ bigger than one, we consider a $q$-difference version of a second-order singular differential operator which depends on a real parameter. We give three exact parameter intervals in which the operator is semibounded from above, not semibounded, and semibounded from below, respectively. We also provide two exact pararameter sets in which the operator is symmetric and self adjoint, respectively. Our model exhibits a more complex behaviour than in the classical continuous case but reduces to it when $q$ approaches one.