H 型群球面均值的注入性

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Fourier Analysis and Applications Pub Date : 2024-05-30 DOI:10.1007/s00041-024-10089-9

E. K. Narayanan, P. K. Sanjay, K. T. Yasser

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引用次数: 0

摘要

我们建立了 H 型群 G 上三种不同球均值的注入性结果。第一种是标准球均值算子，它被定义为函数在中心补集球面上的平均值；第二种是在中心球面与其补集球面乘积上的平均值；第三种是在 G 上由同质规范定义的球面上的平均值。如果 m 是 G 的中心维数，那么在 \(1 \le p \le \frac{2m}{m-1}\) 的范围内，这些球面均值的注入性将得到证明。举例说明了我们在前两种情况下的结果的尖锐性。

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Injectivity of Spherical Means on H-Type Groups

We establish injectivity results for three different spherical means on an H-type group, G. The first one is the standard spherical mean operator, which is defined as the average of a function over the spheres in the complement of the center, the second one is the average over the product of spheres in the center and its complement, and the third one is the average over the spheres defined by a homogeneous norm on G. If m is the dimension of the center of G, injectivity of these spherical means is proved for the range \(1 \le p \le \frac{2m}{m-1}\). Examples are provided to show the sharpness of our results in the first two cases.

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来源期刊

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications