超空间中的Radon变换和Dirac分布

IF 2 2区数学 Q1 MATHEMATICS

Analysis and Applications Pub Date : 2021-07-12 DOI:10.1142/s0219530521500305

Al'i Guzm'an Ad'an, I. Sabadini, F. Sommen

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引用次数: 0

摘要

在本文中，我们得到了超空间中delta分布的平面波分解，条件是超维不是奇数和负的。在这些情况下，这种分解允许超Radon变换的显式反演公式。此外，我们还证明了一个更通用的Radon反演公式对超维的所有可能的整数值都有效。这一结果的证明伴随着对超拉普拉斯算子的分数次幂、它们的基本解以及超Riesz核的平面波分解的研究而来。

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On the Radon transform and the Dirac delta distribution in superspace

In this paper, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon transform in these cases. Moreover, we prove a more general Radon inversion formula valid for all possible integer values of the superdimension. The proof of this result comes along with the study of fractional powers of the super Laplacian, their fundamental solutions, and the plane wave decompositions of super Riesz kernels.

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来源期刊

Analysis and Applications 数学-数学

CiteScore

3.90

自引率

4.50%

发文量

审稿时长

>12 weeks

期刊介绍： Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.