A notion of capacity which characterizes removable singularities

Abstract

In this paper the authors define a capacity for a given linear partial differential operator acting on a Banach space of distributions. This notion has as special cases Newtonian capacity, analytic capacity, and <italic>AC</italic> capacity. It is shown that the sets of capacity zero are precisely those sets which are removable sets for the corresponding homogeneous equation. Simple properties of the capacity are derived and special cases examined.

Identifiers

DOI

10.1090/s0002-9947-1972-0306740-4

Citations and references