与频率无关的高斯三角多项式约束及其应用

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-10-22 DOI:10.1016/j.jfa.2024.110705

Fanhao Kong , Wenhao Zhao

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引用次数: 0

摘要

我们证明了一类奇异高斯随机场的三角函数与频率无关的约束，该约束自然产生于奇异随机 PDE 的弱普遍性问题。这使我们能够将海尔-徐（Hairer-Xu）和富兰-古比内利（Furlan-Gubinelli）先前研究中对 KPZ 和动力学 Φ34 中微观模型非线性（路径收敛性）的正则性假设简化为 PDE 结构所要求的启发式最优阈值。

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A frequency-independent bound on trigonometric polynomials of Gaussians and applications

We prove a frequency-independent bound on trigonometric functions of a class of singular Gaussian random fields, which arise naturally from weak universality problems for singular stochastic PDEs. This enables us to reduce the regularity assumption on the nonlinearity of the microscopic models (for pathwise convergence) in KPZ and dynamical

Φ_{3}^{4}

in the previous works of Hairer-Xu and Furlan-Gubinelli to heuristically optimal thresholds required by PDE structures.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis