In this paper we expound the favourable decision of Kamke's (Камке) hypothesis that self-adjoint boundary conditions are regular and we also establish an analogue of Jordan-Dirichlet theorem on uniform convergence of trigonometric Fourier series for the case of the expansions in eigen functions of self-adjoint integral operators from the certain class.
For the integral operator, which kernel has jump discontinuities on the sides and diagonals of the four equal subsquares of the unit square 0 ≤ x, t ≤ 1, Riesz basisness of its eigen and associated functions is proved.
