The N-Dimensional Uncertainty Principle for the Free Metaplectic Transformation

Rui Jing, Bei Liu, Rui Li and Rui Liu
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Rui Jing: College of Science, Tianjin University of Technology, Tianjin 300384, China
Bei Liu: College of Science, Tianjin University of Technology, Tianjin 300384, China
Rui Li: College of Science, Tianjin University of Technology, Tianjin 300384, China
Rui Liu: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

Mathematics, 2020, vol. 8, issue 10, 1-15

Abstract: The free metaplectic transformation is an N-dimensional linear canonical transformation. This transformation operator is useful, especially for signal processing applications. In this paper, in order to characterize simultaneously local analysis of a function (or signal) and its free metaplectic transformation, we extend some different uncertainty principles (UP) from quantum mechanics including Classical Heisenberg’s uncertainty principle, Nazarov’s UP, Donoho and Stark’s UP, Hardy’s UP, Beurling’s UP, Logarithmic UP, and Entropic UP, which have already been well studied in the Fourier transform domain.

Keywords: free metaplectic transformation; uncertainty principle; Nazarov’s UP; Logarithmic’s UP; Beurling’s UP (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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