# Kergin interpolation

### (aka Real and complex mean value interpolation)

This page is dedicated to Kergin interpolation, and more generally to the scale
of mean value interpolations (which includes Hakopian interpolation). These
interpolation schemes, though not of great practical interest (since the
interpolation conditions include various integrals of derivatives), are of
theoretical interest because of their close connection with
Hermite interpolation
(and a widespread interest in developing a theory of multivariate polynomial
interpolation).

## Complex Kergin interpolation

Most of the recent work involves complex Kergin interpolation. The issues
considered so far, are what conditions on the geometry of the domain are
necessary and sufficient for mean value interpolants to be defined on
holomorphic functions, and under
what conditions does the sequence of interpolants converge locally uniformly
to the function being approximated (as the number of points increases).
People working on such questions include
- Tom Bloom (bloom@math.toronto.edu)
- Jean-Paul Calvi (calvi@cict.fr)
- Norm Levenberg (levenber@math.auckland.ac.nz)
- Swedish complex analysts including
- Mats Andersson (matsa@math.chalmers.se)
- Lars Filipsson (filip@fredholm.math.kth.se)
- Mikael Passare (passare@matematik.su.se)

## Representing mean value interpolants and L_p-error bounds

Other work includes representing mean value interpolants (in terms of the
interpolation conditions), obtaining L_p-error bounds for the interpolants,
and estimating the uniform norm of the mean value interpolation operator.
People working on such questions include
- Alan Augel (augel@univ-rennes1.fr)
- Len Bos (lpbos@acs.ucalgary.ca)
- Ulrike Maier (umaier@math.uni-dortmund.de)
- Paul Sablonniere (sablonniere@univ-rennes1.fr)
- Shayne Waldron
(waldron@math.auckland.ac.nz)

## References

This document is maintained by
Shayne
(waldron@math.auckland.ac.nz).
Last Modified: .