Toeplitz operators on higher Cauchy-Riemann spaces
type: Item
instance of: scholarly article
title: Toeplitz operators on higher Cauchy-Riemann spaces
author: Miroslav Engliš
author: Genkai Zhang
published in: Documenta Mathematica
publication date: 2017-11-21T00:00:00Z
review text: Summary: We develop a theory of Toeplitz, and to some extent Hankel, operators on the kernels of powers of the boundary d-bar operator, suggested by Boutet de Monvel and Guillemin, and on their analogues, somewhat better from the point of view of complex analysis, defined using instead the covariant Cauchy-Riemann operators of Peetre and the second author. For the former, Dixmier class membership of these Hankel operators is also discussed. Our main tool are the generalized Toeplitz operators (with pseudodifferential symbols), in particular there appears naturally the problem of finding parametrices of matrices of such operators in situations when the principal symbol fails to be elliptic.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 32W25
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 32W10
zbMATH DE Number: 6810405
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Hankel operator
zbMATH Keywords: Cauchy-Riemann operators
MaRDI profile type: Publication
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DOI: 10.25537/DM.2017V22.1081-1116
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description: scientific article; zbMATH DE number 6810405