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TOEPLITZ OPERATORS ON HIGHER CAUCHY-RIEMANN SPACES

M. Englis ; Genkai Zhang (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori)
Documenta Mathematica (1431-0643). Vol. 22 (2017), p. 1081-1116.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Toeplitz operator, Hankel operator, Cauchy-Riemann operators



Denna post skapades 2017-11-21.
CPL Pubid: 253269

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)

Ämnesområden

Matematik

Chalmers infrastruktur