On Complex Analytic tools, and the Holomorphic Rotation methods
Classical Analysis and ODEs
2022-10-06 v1
Abstract
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It is known [6] that all harmonic functions in higher dimensions are combinations of holomorphic functions on 2 dimensional planes, extended as, constant in normal directions. We derive representation theorems, with corresponding isometries, opening the door for applications in higher dimensions, to the processing of highly oscillatory multidimensional signals.
Keywords
Cite
@article{arxiv.2210.01949,
title = {On Complex Analytic tools, and the Holomorphic Rotation methods},
author = {Ronald R. Coifman and Jacques Peyrière and Guido Weiss},
journal= {arXiv preprint arXiv:2210.01949},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2101.05311