Jacob's ladder as generator of new class of iterated $L_2$-orthogonal systems and their dependence on the Riemann's function

Abstract

In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is new one in the theory of the Riemann's zeta-function and simultaneously in the theory of $L_2$-orthogonal systems.