Conditions for convergence of biorthogonal expansions of functions on a closed interval (Q5951380)

The author considers a differential operator induced by the differential expression \[ d^{2n}/dx^{2n} + \sum_{l=1}^{2n}p_l(x)d^{2n-l}/dx^{2n-l} \] on the interval \(x\in(0,1)\). He studies systems of generalized root functions of the operator under assumptions that do not provide the basis property of the systems. He gives an estimate on the difference between the biorthogonal expansion associated with a system of the root functions and the corresponding trigonometric Fourier series expansion, which, in particular, shows the convergence of such expansions and gives the rate of convergence.