Carlemann Approximation on Riemann Surfaces.
The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².
Given a homogeneous elliptic partial differential operator L of order two with constant complex coefficients in R2, we consider entire solutions of the equation Lu = 0 for which limr→∞ u(reiφ) =: U(eiφ) exists for all φ ∈ [0; 2π) as a finite limit in C. We characterize the possible "radial limit functions" U. This is an analog of the work of A. Roth for entire holomorphic functions. The results...
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