Rational approximation near zero sets of functions.
The paper deals with the relation between global rational approximation and local approximation off the zero set. Also connections with the problem f ∈ R(X) ⇒ f ∈ R(X) are studied.
On radial limit functions for entire solutions of second order elliptic equations in R.
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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