p-Adic interpolation and approximation of a continuous function by linear combinations of shifts of p-adic valuations Original Research Article

In this work, questions about interpolation and approximation of a continuous function f:Zp→R (f:Zp→Qp) by functions of the form ∑k=1Nλk|x−xk|p are discussed. The theorem about uniform approximation of a continuous function f:Zp→R is proved. Nonexistence of such approximation for a Qp-valued function is shown.