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

TL;DR

This paper introduces a novel class of $L_2$-orthogonal functions generated through iterated systems using Jacob's ladders and the Riemann zeta-function, advancing both orthogonal systems theory and zeta-function analysis.

Contribution

It presents a new method for constructing $L_2$-orthogonal systems based on Jacob's ladders and the Riemann zeta-function, offering novel insights in both areas.

Findings

New $L_2$-orthogonal systems constructed

Connection between Jacob's ladders and zeta-function established

Advances in orthogonal systems and zeta-function theory

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.