Discrete Ingham type inequalities with a weakened gap condition

Ingham type inequalities in lattices

A classical theorem of Ingham extended Parseval's formula of the trigonometrical system to arbitrary families of exponentials satisfying a uniform gap condition. Later his result was extended to several dimensions, but the optimal integration domains have only been determined in very few cases. The purpose of this paper is to determine the optimal connected integration domains for all regular two-dimensional lattices.

曲面Ingham不等式与环面Schrödinger方程的观测性

Curved Ingham Inequalities for Dispersive Trigonometric Sums

研究通过曲面时空轨迹实现环面Schrödinger方程的观测，建立新的三角和上下界，揭示低频和高频成分的观测特性。

From the Ingham--Jessen property to mixed-mean inequalities

For every symmetric mean $\mathscr{M} \colon \bigcup_{n=1}^\infty I^n \to I$ (where $I$ an interval) and a nonzero function $W \colon \{1,\dots,n\} \to \mathbb{N} \cup \{0\}$, define an $n$-variable mean by $$\mathscr{M}_W(x):=\mathscr{M}\big(\underbrace{x_1,\dots,x_1}_{W(1)\text{-times}},\dots,\underbrace{x_n,\dots,x_n}_{W(n)\text{-times}}\big) \text{ for }x=(x_1,\dots,x_n) \in I^n.$$ Given two symmetric means $\mathscr{M},\,\mathscr{N} \colon \bigcup_{n=1}^\infty I^n \to I$ satisfying the so-called Ingham--Jessen inequality and some nonzero functions $F_1,\dots,F_k$, $G_1,\dots,G_l \colon \{…

从 Ingham 到 Nazarov 不等式：关于若干三角不等式的一个综述

From Ingham to Nazarov's inequality: a survey on some trigonometric inequalities

本文综述了调和与非调和三角多项式在 L^1 和 L^2 范数下的若干不等式，重点介绍 Ingham 不等式、Littlewood 猜想的证明及 Nazarov 的非调和对应结果，并补充了小区间上的定量估计与更强条件下的下界。