Exterior Euler summability

We define and study a summability procedure that is similar to Euler summability but applied in the exterior of a disc, not in the interior. We show that the procedure is well defined and that it actually has many interesting properties. We use these ideas to study some problems of analytic continuation and to give a construction of the convex support of an analytic functional. We also use this exterior summability to study Mittag–Leffler developments.