A class of Toeplitz operators in several complex variables

Dmitrii P. Fedchenko

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: In order to study the Toeplitz algebras related to a Dirac operators in a neighborhood of a closed bounded domain $\mathcal{D}$ with smooth boundary in $\mathbb{C}^n$ we introduce a singular Cauchy type integral. We compute its principal symbol, thus initiating the index theory.

Keywords: Dirac operators, Cauchy type integral, symbol, Toeplitz operators, index.

UDC: 517.983.24

Received: 10.10.2016
Received in revised form: 14.11.2016
Accepted: 20.02.2017

Language: English

DOI: 10.17516/1997-1397-2017-10-2-206-215

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