A notion of capacity which characterizes removable singularities

Harvey, Reese; Polking, John C.

doi:10.1090/S0002-9947-1972-0306740-4

A notion of capacity which characterizes removable singularities
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by Reese Harvey and John C. Polking PDF

Trans. Amer. Math. Soc. 169 (1972), 183-195 Request permission

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 AC 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.

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