Abstract:
n this paper, we have been interested in the commutativity and spectral properties
of two higher order symmetric differential operators with unbounded coefficients.
By constructing appropriate comparison algebras of the corresponding self-adjoint
operator extensions and application of asymptotic integration, under suitable decay
and growth conditions imposed on the coefficients, we have deduced that the operators
commute if they are of the same order and the absolutely continuous spectrum of their
self-adjoint extensions is the whole of real line. Using some examples, we have shown
that some necessary conditions cannot be weakened further.