Necessary and sufficient conditions for the Riesz basis property of the eigen- and associated functions of high-order differential operators on an interval (Q951724)

The author considers formally non-selfadjoint differential operator \[ Lu=u^{(n)}(x)+p_{1}(x)u^{(n-1)}(x)+\cdots +p_{n}(x)u(x),\quad n\geq 2, \] on an arbitrary finite interval \(G\) of the real line. Necessary and sufficient conditions for the Riesz basis property of systems of eigen- and associated functions of \(L\) are established in terms of the Fourier coefficients and the norms of system elements in other spaces.