## Taiwanese Journal of Mathematics

### Algebraic Properties of Cauchy Singular Integral Operators on the Unit Circle

Caixing Gu

#### Abstract

In this paper we study algebraic properties of singular integral operators with Cauchy kernel on the $L^{2}$ space of the unit circle. We give an operator equation characterization for this class of Cauchy singular integral operators. This characterization provides a direct connection between the singular integral operators and multiplication operators. We then use this characterization to study when two Cauchy singular integral operators commute. Our approach also leads to generalizations of several results on normal Cauchy singular integral operators obtained recently by Nakazi and Yamamoto.

#### Article information

Source
Taiwanese J. Math., Volume 20, Number 1 (2016), 161-189.

Dates
First available in Project Euclid: 1 July 2017

https://projecteuclid.org/euclid.twjm/1498874427

Digital Object Identifier
doi:10.11650/tjm.20.2016.6188

Mathematical Reviews number (MathSciNet)
MR3462873

Zentralblatt MATH identifier
1357.45010

#### Citation

Gu, Caixing. Algebraic Properties of Cauchy Singular Integral Operators on the Unit Circle. Taiwanese J. Math. 20 (2016), no. 1, 161--189. doi:10.11650/tjm.20.2016.6188. https://projecteuclid.org/euclid.twjm/1498874427

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