Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces

Shyam Swarup Mondal; Anirudha Poria

doi:10.1002/mma.8376

Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces

Shyam Swarup Mondal
, Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

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

4 Citations (Scopus)

Abstract

The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain Cowling–Price's, Hardy's and Morgan's uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based on versions of the Phragmén–Lindlöf type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi–Cherednik operator.

Original language	English
Pages (from-to)	10424-10439
Number of pages	16
Journal	Mathematical Methods in the Applied Sciences
Volume	45
Issue number	16
DOIs	https://doi.org/10.1002/mma.8376
Publication status	Published - 15 Nov 2022

Keywords

Cowling–Price's theorem
Hardy's theorem
Morgan's theorem
weighted modulation spaces
windowed Opdam–Cherednik transform

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10.1002/mma.8376

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@article{dcc812041bda474baeaf42c9488be29a,

title = "Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces",

abstract = "The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain Cowling–Price's, Hardy's and Morgan's uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based on versions of the Phragm{\'e}n–Lindl{\"o}f type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi–Cherednik operator.",

keywords = "Cowling–Price's theorem, Hardy's theorem, Morgan's theorem, weighted modulation spaces, windowed Opdam–Cherednik transform",

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

note = "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. Research was supported by the European Research Council Starting Grant No. 713927. 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. Research was supported by the European Research Council Starting Grant No. 713927. Publisher Copyright: {\textcopyright} 2022 John Wiley \& Sons, Ltd.",

year = "2022",

month = nov,

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doi = "10.1002/mma.8376",

language = "English",

volume = "45",

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journal = "Mathematical Methods in the Applied Sciences",

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T1 - Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces

AU - Mondal, Shyam Swarup

AU - Poria, Anirudha

N1 - 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. Research was supported by the European Research Council Starting Grant No. 713927. 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. Research was supported by the European Research Council Starting Grant No. 713927. Publisher Copyright: © 2022 John Wiley & Sons, Ltd.

PY - 2022/11/15

Y1 - 2022/11/15

N2 - The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain Cowling–Price's, Hardy's and Morgan's uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based on versions of the Phragmén–Lindlöf type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi–Cherednik operator.

AB - The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces associated with this transform. In particular, we obtain Cowling–Price's, Hardy's and Morgan's uncertainty principles for this transform on weighted modulation spaces. The proofs of the results are based on versions of the Phragmén–Lindlöf type result for several complex variables on weighted modulation spaces and the properties of the Gaussian kernel associated with the Jacobi–Cherednik operator.

KW - Cowling–Price's theorem

KW - Hardy's theorem

KW - Morgan's theorem

KW - weighted modulation spaces

KW - windowed Opdam–Cherednik transform

UR - https://www.scopus.com/pages/publications/85129906632

U2 - 10.1002/mma.8376

DO - 10.1002/mma.8376

M3 - Article

AN - SCOPUS:85129906632

SN - 0170-4214

VL - 45

SP - 10424

EP - 10439

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -

Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces

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Keywords

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