Taiwanese Journal of Mathematics

Algebraic Properties of Cauchy Singular Integral Operators on the Unit Circle

Caixing Gu

Full-text: Open access

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

Permanent link to this document
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

Subjects
Primary: 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 47L05: Linear spaces of operators [See also 46A32 and 46B28] 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Keywords
singular integral operator Cauchy kernel Toeplitz operator Hankel operator normal operator

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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References

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