Περίληψη:
We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on products K=∏i=1dKi, where Ki⊆ C are compact sets and C\ Ki are connected, i= 1 , … , d and 0 ∉ K. On such K the partial sums approximate uniformly any polynomial. Finally, the partial sums may be replaced by more general expressions. The phenomenon is topologically and algebraically generic. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, AT part of Springer Nature.
