Abstract: We describe a recent evolution of Harmonic Analysis to generate analytic tools for the joint organization of the geometry of subsets of R n and the analysis of functions and operators on the subsets. In this analysis we establish a duality between the geometry of functions and the geometry of the space. The methods are used to automate various analytic organizations, as well as to enable informative data analysis. These tools extend to higher order tensors, to combine dynamic analysis of changing structures. In particular we view these tools as necessary to enable automated empirical modeling, in which the goal is to model dynamics in nature, ab initio, through observations alone. We will illustrate recent developments in which physical models can be discovered and modelled directly from observations, in which the conventional Newtonian differential equations, are replaced by observed geometric data constraints. This work represents an extended global collaboration including, recently, A. Averbuch, A. Singer, Y. Kevrekidis, R. Talmon, M. Gavish, W. Leeb, J. Ankenman, G. Mishne and many more.
https://eta.impa.br/dl/PL018.pdf
本文描述R^n中子集的调和分析的发展。这些方法综合了几何，组合，概率和调和分析。它出现在数据分析或信号处理中，作为分析高维空间中大数据集的几何性质，并分析在这些数据集上定义的函数性质的工具。由此它位于数学，计算机科学和工程的几个分支的交叉点上。
相关附件
10-PL018 Coifman
