functional-differential operator

On the Same Theorem on a Equiconvergence at the Whole Segment for the Functional Differential Operators

Authors: Burlutskaya M. S., Khromov A. P.

The equiconvergence of expansions in eigen- and adjoint functions of functional-differential operator with involution, containing the potentials, and simplest functional-differential operator at the whole segment of Fourier series is established.

Jordan–Dirichlet Theorem for Functional Differential Operator with Involution

Authors: Burlutskaya M. S.

In this paper the problem of decomposability of a function f(x) into Fourier series with respect to the system of eigenfunctions of a functional-differential operator with involution Ly = y′(1 − x) + ®y′(x) + p1(x)y(x) + p2(x)y(1−x), y(0) = °y(1) is investigated. Based on the study of the resolvent of the operator easier and using the method of contour integration of the resolvent, we obtain the sufficient conditions for the convergence of the Fourier series for a function f(x) (analogue of the Jordan–Dirichlet’s theorem).