Scholarlink

An extended holomorphic Radon transform enables a “method of rotations” to lift one dimensional adapted nonlinear holomorphic analysis tools to higher dimensions. In particular the various multiscale orthogonal bases of holomorphic functions in Hardy spaces in one dimension give rise to orthogonal bases of Harmonic functions on higher dimensional half spaces. We provide an overview of recent progress in nonlinear approximation using holomorphy, and discuss their extension to high dimension through the Radon transform.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Complex Analytic Tools, and the Holomorphic Rotation Methods

  • 章节

  • 发表日期：

    2025年

查看全文
  • Ronald R. Coifman,
  • Jacques Peyrière,
  • Guido Weiss

摘要

An extended holomorphic Radon transform enables a “method of rotations” to lift one dimensional adapted nonlinear holomorphic analysis tools to higher dimensions. In particular the various multiscale orthogonal bases of holomorphic functions in Hardy spaces in one dimension give rise to orthogonal bases of Harmonic functions on higher dimensional half spaces. We provide an overview of recent progress in nonlinear approximation using holomorphy, and discuss their extension to high dimension through the Radon transform.