两步零序列的分析

摘要：

零序列产生于研究与弗斯滕伯格的塞梅雷迪定理证明相关的多重遍历平均数，并在加法组合学中发挥了作用。零序列是概周期序列的推广，我们研究了经典的概周期序列理论中的哪些部分可以推广到两步零序列。本文阐述并证明了二步诣零序列的基本性质，给出了二步诣零序列的一个分类方案。

英文摘要：

Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg's proof of Szemerédi's Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for 2-step nilsequences and give a classification scheme for them.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。