Cauchy kernel

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The function of the form , which is the kernel of the Cauchy integral. In the case of the unit circle one has the following relationship between the Cauchy kernel and the Hilbert kernel:


The term Cauchy kernel is sometimes applied to the function


See also Kernel function; Kernel of an integral operator.


[a1] A.I. Markushevich, "Theory of functions of a complex variable" , 1–3 , Chelsea (1977) (Translated from Russian)
[a2] E.C. Titchmarsh, "Introduction to the theory of Fourier integrals" , Oxford Univ. Press (1948)
[a3] W. Rudin, "Real and complex analysis" , McGraw-Hill (1974) pp. 24
How to Cite This Entry:
Cauchy kernel. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article