The spectrum of differential operators of order \(2n\) with almost constant coefficients (Q5946979)

The authors study spectral properties of operators generated by selfadjoint ordinary differential expressions of arbitrary order. The paper focuses on a generalization of results for second-order operators concerning conditions under which the spectral properties of the operator are essentially the same as the ones of the related constant coefficient differential operator; namely, the singular continuous spectrum is empty, whereas the absolutely continuous part of the operator is unitary equivalent to the constant coefficient operator. The proof is based on using the asymptotic integration technique applied for computing (approximately) the related Titchmarsh-Weyl \(M\)-functions. Special attention is paid to uniform estimates on the error terms from the limiting behavior of \(M(z)\) as a complex \(z\) approaches the spectrum.