Nonlinear harmonic analysis and dispersive partial differential equations

这项建议致力于线性和非线性调和分析。它的目的是统一调和分析中最重要的属性，如约束估计、微分算子的色散性质、谱乘子、一致Sobolev估计和夏普Weyl公式。这种统一将有力地改进所有技术和科学领域的数学建模工具。值得注意的应用包括医学成像、流体动力学和使用量子解释的亚原子建模。 它将解决偏微分算子谱分析中的几个重要公开问题，并将发展调和分析的新的前沿技术，并将其应用于非线性偏微分方程。

This proposal is devoted to linear and nonlinear harmonic analysis. It aims to unify the most significant attributes of harmonic analysis such as restriction estimates, dispersive properties of differential operators, spectral multipliers, uniform Sobolev estimates and sharp Weyl formula. Such unification will strongly improve tools for mathematical modelling in all areas of technology and science. Notable applications include medical imaging, fluid dynamics and subatomic modelling using quantum interpretation. It will solve several important open problems in spectral analysis of partial differential operators and develop new cutting-edge techniques in harmonic analysis with application to nonlinear partial differential equations.