估值的傅立叶变换是傅立叶变换

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-11-06 DOI:10.1016/j.jfa.2024.110741

Dmitry Faifman , Thomas Wannerer

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引用次数: 0

摘要

阿列斯克证明了平移不变光滑值空间存在一个显著的同构，它具有与经典傅里叶变换相同的函数性质。在本文中，我们展示了如何直接用函数的傅里叶变换来描述这种同构。因此，我们得到了 Alesker-Fourier 变换主要性质的简单证明。其中一个性质以前只是阿莱克斯克的猜想，本文首次证明了它。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Fourier transform on valuations is the Fourier transform

Alesker has proved the existence of a remarkable isomorphism of the space of translation-invariant smooth valuations that has the same functorial properties as the classical Fourier transform. In this paper, we show how to directly describe this isomorphism in terms of the Fourier transform on functions. As a consequence, we obtain simple proofs of the main properties of the Alesker–Fourier transform. One of these properties was previously only conjectured by Alesker and is proved here for the first time.

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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