A Contribution to Best Approximation in the l2 - Norm
For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best -approximation with an unbounded number of finite poles are considered.
For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.