2019/06/04 by Firdous A. Shah, Shah, Firdous A., Azhar Y. Tantary +1
Computer Science · Earth and Planetary Sciences · Mathematics · #26D10. 35A23. 42B10. 42C40. 42A38 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1906.01263
openalex publication_date 2019/06/04 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
The aim of this article is to formulate some novel uncertainty principles for\nthe continuous shearlet transforms in arbitrary space dimensions. Firstly, we\nderive an analogue of the Pitt's inequality for the continuous shearlet\ntransforms, then we formulate the Beckner's uncertainty principle via two\napproaches: one based on a sharp estimate from Pitt's inequality and the other\nfrom the classical Beckner's inequality in the Fourier domain. Secondly, we\nconsider a logarithmic Sobolev inequality for the continuous shearlet\ntransforms which has a dual relation with Beckner's inequality. Thirdly, we\nderive Nazarov's uncertainty principle for the shearlet transforms which shows\nthat it is impossible for a non-trivial function and its shearlet transform to\nbe both supported on sets of finite measure. Towards the culmination, we\nformulate local uncertainty principles for the continuous shearlet transforms\nin arbitrary space dimensions.\n