The Spectrum Of Two Kinds Of Special2n-th Order Differential Operators With Real Coefficients

First, a kind of differential operators are considered, which are generated by the dif-ferential expression on an interval (-∞,∞) with constant coefficients. It is proved that the operator considered is essentially self-adjoint, and we obtained the distribution of es-sential spectrum of its self-adjoint extensions by using the corresponding embedding the-orems and Fourier transform. Secondly, a kind of differential operators with trigonometric function coefficients are considered. We proved that this kind of differential operator is essentially self-adjoint.