Multiplicity Operators
Complex Variables
2014-06-24 v2 Algebraic Geometry
Differential Geometry
Dynamical Systems
Abstract
For functions of a single complex variable, points of multiplicity greater than are characterized by the vanishing of the first derivatives. There are various quantitative generalizations of this statement, showing that for functions that are in some sense close to having multiplicity greater than , the first derivatives must be small. In this paper we aim to generalize this situation to the multi-dimensional setting. We define a class of differential operators, the \emph{multiplicity operators}, which act on maps from to and satisfy properties analogous to those described above. We demonstrate the usefulness of the construction by applying it to some problems in the theory of Noetherian functions.
Cite
@article{arxiv.1309.1868,
title = {Multiplicity Operators},
author = {Gal Binyamini and Dmitry Novikov},
journal= {arXiv preprint arXiv:1309.1868},
year = {2014}
}