| Abstract: | We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator‐valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator ??s in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of ??s as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices ??s of ??s, interpreted as Mellin‐edge representations of P. Copyright © 2005 John Wiley & Sons, Ltd. |
