Calculation of the coefficients of expansions in derivative chains of a spectral problem (Q1316886)

The communication is devoted to a method of calculation of a function expansion in a series of eigenfunctions of a certain spectral problem for a second order ordinary differential equation. It is introduced a corresponding linear operator on a tensor product of some spaces. A formula for the adjoint operator is obtained and a relation between eigenelements of this operator and of the spectral problem under consideration is established. Finally, formulas for expansion coefficients in terms of eigenelements of the spectral problem and the adjoint one are presented.