The Gauss Image Problem with weak Aleksandrov condition

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-07-31 DOI:10.1016/j.jfa.2024.110611

Vadim Semenov

引用次数: 0

Abstract

We introduce a relaxation of the Aleksandrov condition for the Gauss Image Problem. This weaker condition turns out to be a necessary condition for two measures to be related by a convex body. We provide several properties of the new condition. A solution to the Gauss Image Problem is obtained for the case when one of the measures is assumed to be discrete and the another measure is assumed to be absolutely continuous, under the new relaxed assumption.

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弱阿列克桑德罗夫条件下的高斯图像问题

我们为高斯图像问题引入了阿列克桑德罗夫条件的放松。这个较弱的条件被证明是两个度量通过凸体相关的必要条件。我们提供了新条件的几个性质。在新的放宽假设下，我们得到了其中一个度量是离散的，而另一个度量是绝对连续的情况下高斯图像问题的解。

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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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