Uncertainty principles for the Opdam–Cherednik transform on modulation spaces

Anirudha Poria

doi:10.1080/10652469.2020.1813129

Uncertainty principles for the Opdam–Cherednik transform on modulation spaces

Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Indian Institute of Science Bangalore

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

11 Citations (Scopus)

Abstract

In this paper, we establish the Cowling–Price's, Hardy's and Morgan's uncertainty principles for the Opdam–Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of the heat kernel associated with the Jacobi–Cherednik operator and the versions of the Phragmén–Lindlöf type result for the modulation spaces.

Original language	English
Pages (from-to)	191-206
Number of pages	16
Journal	Integral Transforms and Special Functions
Volume	32
Issue number	3
DOIs	https://doi.org/10.1080/10652469.2020.1813129
Publication status	Published - 2021

Keywords

33C45
42B35
43A32
44A15
Cowling–Price's theorem
Hardy's theorem
modulation spaces
Morgan's theorem
Opdam–Cherednik transform

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10.1080/10652469.2020.1813129

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title = "Uncertainty principles for the Opdam–Cherednik transform on modulation spaces",

abstract = "In this paper, we establish the Cowling–Price's, Hardy's and Morgan's uncertainty principles for the Opdam–Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of the heat kernel associated with the Jacobi–Cherednik operator and the versions of the Phragm{\'e}n–Lindl{\"o}f type result for the modulation spaces.",

keywords = "33C45, 42B35, 43A32, 44A15, Cowling–Price's theorem, Hardy's theorem, modulation spaces, Morgan's theorem, Opdam–Cherednik transform",

author = "Anirudha Poria",

note = "Funding Information: The author is deeply indebted to Prof. S. Thangavelu for several fruitful discussions and generous comments. The author is grateful to the University Grants Commission, India for providing the Dr D. S. Kothari Post Doctoral Fellowship (Award No.- F.4-2/2006 (BSR)/MA/18-19/0032). The author also wishes to thank the anonymous referee for valuable comments and suggestions which helped to improve the quality of the paper. Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2021",

doi = "10.1080/10652469.2020.1813129",

language = "English",

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pages = "191--206",

journal = "Integral Transforms and Special Functions",

issn = "1065-2469",

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T1 - Uncertainty principles for the Opdam–Cherednik transform on modulation spaces

AU - Poria, Anirudha

N1 - Funding Information: The author is deeply indebted to Prof. S. Thangavelu for several fruitful discussions and generous comments. The author is grateful to the University Grants Commission, India for providing the Dr D. S. Kothari Post Doctoral Fellowship (Award No.- F.4-2/2006 (BSR)/MA/18-19/0032). The author also wishes to thank the anonymous referee for valuable comments and suggestions which helped to improve the quality of the paper. Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - In this paper, we establish the Cowling–Price's, Hardy's and Morgan's uncertainty principles for the Opdam–Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of the heat kernel associated with the Jacobi–Cherednik operator and the versions of the Phragmén–Lindlöf type result for the modulation spaces.

AB - In this paper, we establish the Cowling–Price's, Hardy's and Morgan's uncertainty principles for the Opdam–Cherednik transform on modulation spaces associated with this transform. The proofs of the theorems are based on the properties of the heat kernel associated with the Jacobi–Cherednik operator and the versions of the Phragmén–Lindlöf type result for the modulation spaces.

KW - 33C45

KW - 42B35

KW - 43A32

KW - 44A15

KW - Cowling–Price's theorem

KW - Hardy's theorem

KW - modulation spaces

KW - Morgan's theorem

KW - Opdam–Cherednik transform

UR - https://www.scopus.com/pages/publications/85090083655

U2 - 10.1080/10652469.2020.1813129

DO - 10.1080/10652469.2020.1813129

M3 - Article

AN - SCOPUS:85090083655

SN - 1065-2469

VL - 32

SP - 191

EP - 206

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

IS - 3

ER -

Uncertainty principles for the Opdam–Cherednik transform on modulation spaces

Abstract

Keywords

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