Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient

Abstract

We show that selfadjoint operator extensions of minimal second order differ ence operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.