quadratic pencil of differential operators
We consider the quadratic strongly irregular pencil of ordinary second order differential operators with constant coefficients and with a multiple root of the characteristic equation. The amounts of double expansions in biorthogonal Fourier series in the derived chains of such pencils and a necessary and sufficient condition for convergence of these expansions to the expanded vector-valued function are found. This necessary and sufficient condition is a differential equation relating the components of the expanded vector function.
We consider a quadratic strongly irregular pencil of 2-d order ordinary differential operators with constant coefficients and positive roots of the characteristic equation. Both the amounts of double expansions in a series in the derivative chains of such pencils and necessary and sufficient conditions for convergence of these expansions to the decomposed vector-valued function are found.
