Toeplitz operators on higher Cauchy-Riemann spaces

@article{29845,
   author = {Engliš, Miroslav and Genkai, Zhang},
   article_location = {Bielefeld},
   article_number = {2017},
   keywords = {Toeplitz operator; Hankel operator; Cauchy-Riemann operators},
   language = {eng},
   issn = {1431-0643},
   journal = {Documenta Mathematica},
   title = {Toeplitz operators on higher Cauchy-Riemann spaces},
   url = {https://www.math.uni-bielefeld.de/documenta/vol-22/32.html},
   volume = {22},
   year = {2017}
}

TY  - JOUR
ID  - 29845
AU  - Engliš, Miroslav - Genkai, Zhang
PY  - 2017
TI  - Toeplitz operators on higher Cauchy-Riemann spaces
JF  - Documenta Mathematica
VL  - 22
IS  - 2017
SP  - 1081-1116
EP  - 1081-1116
PB  - Deutsche Mathematiker Vereinigung
SN  - 14310643
KW  - Toeplitz operator
KW  - Hankel operator
KW  - Cauchy-Riemann operators
UR  - https://www.math.uni-bielefeld.de/documenta/vol-22/32.html
L2  - https://www.math.uni-bielefeld.de/documenta/vol-22/32.html
N2  - 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.
ER  - 

ENGLIŠ, Miroslav and Zhang GENKAI. Toeplitz operators on higher Cauchy-Riemann spaces. \textit{Documenta Mathematica}. Bielefeld: Deutsche Mathematiker Vereinigung, 2017, vol.~22, No~2017, p.~1081-1116. ISSN~1431-0643.