# Cauchy kernel

From Encyclopedia of Mathematics

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:

where

The term Cauchy kernel is sometimes applied to the function

#### Comments

See also Kernel function; Kernel of an integral operator.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Cauchy_kernel&oldid=18064

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article