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Sharp Hausdorff-Young inequalities for the quaternion Fourier transforms

Author: P. Lian
Journal: Proc. Amer. Math. Soc. 148 (2020), 697-703
MSC (2010): Primary 42B10, 42A05
Published electronically: August 7, 2019
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Abstract: The quaternion Fourier transforms are powerful tools in modern data analysis, in particular for color image processing. At present, there are mainly three different quaternion Fourier transforms widely used. In this paper, we prove the sharp Hausdorff-Young inequalities for these three transforms and the more general ones, i.e., the steerable quaternion Fourier transforms. Then Hirschman's entropy uncertainty principle in the quaternion setting follows from the standard differential approach.

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P. Lian
Affiliation: School of Mathematical Sciences, Tianjin Normal University, Binshui West Road 393, Tianjin 300387, People’s Republic of China

Keywords: Quaternion Fourier transform, uncertainty principle, Hausdorff-Young inequality
Received by editor(s): April 29, 2019
Received by editor(s) in revised form: May 26, 2019
Published electronically: August 7, 2019
Additional Notes: The author was supported by the TJNU starting grant 5RL155.
Communicated by: Ariel Barton
Article copyright: © Copyright 2019 American Mathematical Society