Uncertainty principles associated with the short time quaternion coupled fractional Fourier transform

2023/07/03 by Bivek Gupta, Amit Verma, Gupta, Bivek +3
Mathematics · Physics and Astronomy · #11R52 #42A05 #42B10 #Advanced Differential Geometry Research #FOS: Mathematics #Functional Analysis (math.FA) #General Mathematics (math.GM) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2309.16675

openalex publication_date 2023/07/03 · openalex created_date 2023/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on ℝ⁴ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain the sharp Hausdorff-Young inequality for QCFrFT and obtain the associated Rènyi uncertainty principle. We also define the short time quaternion coupled fractional Fourier transform (STQCFrFT) and explore its important properties followed by the Lieb's and entropy uncertainty principles.

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