Namespaces
Variants
Actions

Cauchy kernel

From Encyclopedia of Mathematics
Revision as of 17:24, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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