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A striking fact about function theory in several variables is that, under suitable convexity hypotheses on a domain C n with n > 1, if z 0 2 is \close" to the boundary @, then there are representing measures for z 0 whose support on @ is compactly supported and \close" to z 0 , the projection of z 0 onto the boundary. This is false for domains in C , for general non-convex domains in C n , and for harmonic functions on domains in R 2n. For a simple example of this phenomenon, let = f(z; w); Re(z) > jwj 2 g. We will denote the boundary of by = fRe(z) = jwj 2 g (the Heisenberg group). We wish to represent the value of a holomorphic function F on at the point (0; r) 2 for r > 0, by integrating F against a suitable measure on. To do this, we let 2 C 1 0 (C) be a radial function with support in the unit disc and whose integral over C is one. Let r (w) = 4 r 2 2(w ? r) r : The function r has support in the disc centered at r with radius r 2 and the integral of r over C is one. The mean value property for holomorphic functions shows that

Local reproducing kernels on wedge-like domains with type 2 edges