From: stephen madden <nmadden@massed.net>
Newsgroups: sci.math.symbolic
Subject: Re: Help. What's a Bergman Reproducing Kernel?
Date: Thu, 26 Mar 1998 01:19:16 +0000

John Warren wrote:

> Any known explanation of the Bergman Reproducing Kernel    Thank you,
> Joan (email to jnwarren@pipeline.com)

  Ref: Bergman, S. and Schiffer, M., Kernel Functions and Elliptic
Differential
Equations in Mathematical Physics.  Academic Press, 1953.

While I don't know what distinguishes a Bergman kernel from others,
kernel functions
arise in solution of many partial differential equations by their
conversion to integral
equations.  Once a conversion has been completed the integral equations
can be
numerically attacked (in the general case) by variational methods or
others such as
Galerkin methods.  A reproducing kernel is one which, when applied to a
member
of a certain class of functions, reproduces the member function.

This is a very loose description, see the reference above or more recent
ones, to
clarify the exposition and find information that more directly addresses
the problem
that elicited your question.