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Characterisation of wave front sets by the Stockwell transform
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jmaa.2020.124329
Sanja Atanasova , Stevan Pilipović , Bojan Prangoski , Katerina Saneva

Abstract We characterise the wave front sets via the Stockwell transform defined as a combination of the short-time Fourier transformation and a special class of rotations. The main results of the first part are necessary and sufficient criteria related to the directional smoothness of a tempered distribution in the cases when the space dimension n equals 1, 2, 4 or 8. In the second part, we extend the results to arbitrary n ∈ Z + .

中文翻译:

通过斯托克韦尔变换表征波前集

摘要 我们通过定义为短时傅立叶变换和特殊类型旋转组合的斯托克韦尔变换来表征波前集。在空间维度 n 等于 1、2、4 或 8 的情况下,第一部分的主要结果是与回火分布的方向平滑性相关的必要且充分的标准。在第二部分中,我们将结果扩展到任意 n ∈ Z + 。
更新日期:2020-10-01
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