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Mexican Hat Wavelet on the Heisenberg Group

2007/05/23 by Azita Mayeli, Mayeli, Azita
Computer Science · Earth and Planetary Sciences · Mathematics · #22E25 #42B20 #42C40 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #math.FA #math.GR #msc:22E25 #msc:42B20 #msc:42C40

paper · pdf · doi:10.48550/arxiv.0705.3364

8 pages, no figures

arxiv created 2007/05/23 · openalex publication_date 2007/05/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article wavelets (admissible vectors) on the Heisenberg group are studied from the point of view of Calderon's formula. Further we shall show that for the class of Schwartz functions the Calderon admissibility condition is equivalent to the usual admissibility property which will be introduced in this work. Furthermore motivated by a well-known example on the real line, the Mexican-Hat wavelet, we demonstrate the existence and construction of an analogous wavelet on the Heisenberg Lie group with 2 vanishing moments, which together with all of its derivatives has Gaussian decay.

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