Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus

Raúl E. Curto; Gopal Datt; Bhawna Bansal Gupta

doi:10.1016/j.bulsci.2024.103466

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Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus

Journal article

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Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus

Raúl E. Curto, Gopal Datt and Bhawna Bansal Gupta

Bulletin des sciences mathématiques, Vol.194, 103466

09/2024

DOI: 10.1016/j.bulsci.2024.103466

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Abstract

We consider Hankel and Toeplitz operators on H2(Tn), the Hardy space of the n-torus Tn. Given symbols φ and ψ in L∞(Tn) with suitable properties, we obtain necessary and sufficient conditions for the Hankel operator Hψ,n and the Toeplitz operator Tφ,n to commute. We then extend the study to the more general situation where no assumptions are imposed on φ, and provide new, non-trivial necessary conditions for the commutativity of Hψ,n and Tφ,n. We also show that certain well known commutativity results between Hankel and Toeplitz operators in the one-variable case do not extend to the multivariable setting.

Commutativity

Hankel operator

Hardy space of n-torus

Toeplitz operator

Details

Title: Subtitle: Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus
Creators: Raúl E. Curto - Department of Mathematics, 225H MLH, The University of Iowa, Iowa City, IA 52242, United States
Gopal Datt - University of Delhi
Bhawna Bansal Gupta - University of Delhi
Resource Type: Journal article
Publication Details: Bulletin des sciences mathématiques, Vol.194, 103466
DOI: 10.1016/j.bulsci.2024.103466
ISSN: 0007-4497
eISSN: 1952-4773
Publisher: Elsevier Masson SAS
Language: English
Electronic publication date: 07/01/2024
Date published: 09/2024
Academic Unit: Mathematics
Record Identifier: 9984652255702771

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