A uniqueness theorem of additive functions and applications to some orthogonal series

TL;DR

This paper proves a uniqueness theorem for additive functions based on derivatives over parallelepipeds and applies it to establish the uniqueness of certain orthogonal series, such as Haar and Price systems.

Contribution

It introduces a new uniqueness theorem for additive functions and applies it to demonstrate the uniqueness of multiple orthogonal series.

Findings

Proved a new uniqueness theorem for additive functions.

Established the uniqueness of Haar and Price orthogonal series.

Applied the theorem to problems in multiple series analysis.

Abstract

The restoration of an additive function defined on P parallelepipeds via its derivative with respect to P parallelepipeds is studied. The obtained theorem is applied to the questions of uniqueness of multiple series with regard to Haar and Price systems.