Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces

Anirudha Poria

doi:10.1080/17476933.2022.2052861

Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces

Anirudha Poria^*

^*Corresponding author for this work

Department of Applied Mathematics

Bar-Ilan University

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

1 Citation (Scopus)

Abstract

In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol ς and two windows functions (Formula presented.) and (Formula presented.). We first present some basic properties of the windowed Opdam–Cherednik transform. Then, we use modulation spaces associated with the Opdam–Cherednik transform as appropriate classes for symbols and windows and study the boundedness and compactness of the localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten–von Neumann class.

Original language	English
Pages (from-to)	1361-1384
Number of pages	24
Journal	Complex Variables and Elliptic Equations
Volume	68
Issue number	8
DOIs	https://doi.org/10.1080/17476933.2022.2052861
Publication status	Published - 2023

Keywords

42B35
47B10
compact operators
localization operators
modulation spaces
Opdam–Cherednik transform
Primary 47G30
Schatten–von Neumann class
Secondary 44A15
windowed Opdam–Cherednik transform

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10.1080/17476933.2022.2052861

Cite this

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title = "Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces",

abstract = "In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol ς and two windows functions (Formula presented.) and (Formula presented.). We first present some basic properties of the windowed Opdam–Cherednik transform. Then, we use modulation spaces associated with the Opdam–Cherednik transform as appropriate classes for symbols and windows and study the boundedness and compactness of the localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten–von Neumann class.",

keywords = "42B35, 47B10, compact operators, localization operators, modulation spaces, Opdam–Cherednik transform, Primary 47G30, Schatten–von Neumann class, Secondary 44A15, windowed Opdam–Cherednik transform",

author = "Anirudha Poria",

note = "Funding Information: Research supported by European Research Council (ERC) Starting Grant No. 713927. The author is deeply indebted to Prof. Nir Lev for several fruitful discussions and generous comments. The author wishes to thank the anonymous referees for their helpful comments and suggestions that helped to improve the quality of the paper. Publisher Copyright: {\textcopyright} 2022 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2023",

doi = "10.1080/17476933.2022.2052861",

language = "English",

volume = "68",

pages = "1361--1384",

journal = "Complex Variables and Elliptic Equations",

issn = "1747-6933",

number = "8",

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T1 - Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces

AU - Poria, Anirudha

N1 - Funding Information: Research supported by European Research Council (ERC) Starting Grant No. 713927. The author is deeply indebted to Prof. Nir Lev for several fruitful discussions and generous comments. The author wishes to thank the anonymous referees for their helpful comments and suggestions that helped to improve the quality of the paper. Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2023

Y1 - 2023

N2 - In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol ς and two windows functions (Formula presented.) and (Formula presented.). We first present some basic properties of the windowed Opdam–Cherednik transform. Then, we use modulation spaces associated with the Opdam–Cherednik transform as appropriate classes for symbols and windows and study the boundedness and compactness of the localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten–von Neumann class.

AB - In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol ς and two windows functions (Formula presented.) and (Formula presented.). We first present some basic properties of the windowed Opdam–Cherednik transform. Then, we use modulation spaces associated with the Opdam–Cherednik transform as appropriate classes for symbols and windows and study the boundedness and compactness of the localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten–von Neumann class.

KW - 42B35

KW - 47B10

KW - compact operators

KW - localization operators

KW - modulation spaces

KW - Opdam–Cherednik transform

KW - Primary 47G30

KW - Schatten–von Neumann class

KW - Secondary 44A15

KW - windowed Opdam–Cherednik transform

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U2 - 10.1080/17476933.2022.2052861

DO - 10.1080/17476933.2022.2052861

M3 - Article

AN - SCOPUS:85127124027

SN - 1747-6933

VL - 68

SP - 1361

EP - 1384

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 8

ER -

Localization operators associated with the windowed Opdam–Cherednik transform on modulation spaces

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Keywords

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