The higher order differential operators in direct sum spaces (Q803912)

The author studies two ordinary differential operators \[ M_ iy=p_{0i}y^{(n)}+p_{1i}y^{(n-1)}+...+p_{ni}y,\quad i=1,2, \] given on intervals \(I_ 1=[a,b]\) and \(I_ 2=[c,d]\) respectively, \(- \infty \leq a<b\leq \infty\), \(-\infty \leq c<d\leq \infty\). Considering these problems on the space \(H=L^ 2(I_ 1)\oplus L^ 2(I_ 2)\) and introducing corresponding minimal \(T_ 0\) and maximal \(T_ M\) operators generated by the pair \((M_ 1,M_ 2)\), he establishes sufficient and necessary conditions for \(T_ 0\) to have a selfadjoint extension in both regular and singular cases. Firstly this problem was considered by \textit{W. N. Everitt} and \textit{A. Zettl} for Sturm-Liouville operators [see Rocky Mt. J. Math. 16, 497-516 (1986; Zbl 0624.34020)].