Uncertainty principles for the windowed Opdam–Cherednik transform

Shyam Swarup Mondal; Anirudha Poria

doi:10.1002/mma.9596

Uncertainty principles for the windowed Opdam–Cherednik transform

Shyam Swarup Mondal, Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study a few versions of the uncertainty principle for the windowed Opdam–Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle, and local uncertainty inequality for this transform. We also obtain the Heisenberg-type uncertainty inequality using the (Formula presented.) -entropy of the windowed Opdam–Cherednik transform.

Original language	English
Pages (from-to)	18861-18877
Number of pages	17
Journal	Mathematical Methods in the Applied Sciences
Volume	46
Issue number	18
DOIs	https://doi.org/10.1002/mma.9596
Publication status	Accepted/In press - 2023

Keywords

Benedicks-type uncertainty principle
Donoho–Stark's uncertainty principle
Heisenberg-type uncertainty inequality
Opdam–Cherednik transform
windowed Opdam–Cherednik transform

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10.1002/mma.9596

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title = "Uncertainty principles for the windowed Opdam–Cherednik transform",

abstract = "In this paper, we study a few versions of the uncertainty principle for the windowed Opdam–Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle, and local uncertainty inequality for this transform. We also obtain the Heisenberg-type uncertainty inequality using the (Formula presented.) -entropy of the windowed Opdam–Cherednik transform.",

keywords = "Benedicks-type uncertainty principle, Donoho–Stark's uncertainty principle, Heisenberg-type uncertainty inequality, Opdam–Cherednik transform, windowed Opdam–Cherednik transform",

author = "Mondal, {Shyam Swarup} and Anirudha Poria",

note = "Funding Information: Research is supported by ERC Starting Grant No. 713927. Funding information Funding Information: The first author gratefully acknowledges the support provided by IIT Guwahati, Government of India. The second author is deeply indebted to Prof. Nir Lev for several fruitful discussions and generous comments. The authors wish to thank the anonymous referees for their helpful comments and suggestions that helped to improve the quality of the paper. Publisher Copyright: {\textcopyright} 2023 John Wiley & Sons Ltd.",

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N2 - In this paper, we study a few versions of the uncertainty principle for the windowed Opdam–Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle, and local uncertainty inequality for this transform. We also obtain the Heisenberg-type uncertainty inequality using the (Formula presented.) -entropy of the windowed Opdam–Cherednik transform.

AB - In this paper, we study a few versions of the uncertainty principle for the windowed Opdam–Cherednik transform. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks-type uncertainty principle, Heisenberg-type uncertainty principle, and local uncertainty inequality for this transform. We also obtain the Heisenberg-type uncertainty inequality using the (Formula presented.) -entropy of the windowed Opdam–Cherednik transform.

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KW - Heisenberg-type uncertainty inequality

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ER -

Uncertainty principles for the windowed Opdam–Cherednik transform

Abstract

Keywords

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