Toeplitz operators on higher Cauchy-Riemann spaces

0481139 - MÚ 2018 RIV DE eng J - Journal Article
Engliš, Miroslav - Zhang, G.
Toeplitz operators on higher Cauchy-Riemann spaces.
Documenta Mathematica. Roč. 22, č. 22 (2017), s. 1081-1116. ISSN 1431-0643. E-ISSN 1431-0643
Institutional support: RVO:67985840
Keywords : Toeplitz operator * Hankel operator * Cauchy-Riemann operators
OECD category: Pure mathematics
Impact factor: 0.918, year: 2017
https://www.math.uni-bielefeld.de/documenta/vol-22/32.html

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.
Permanent Link: http://hdl.handle.net/11104/0276738