Reprint: An interpolation series for continuous functions of a -adic variable (1958)

  • Kurt Mahler


Let be a function on the set of -adic integers. The subset of the non-negative integers is dense on , hence a continuous function on is already determined by its values on , thus also by the numbers In this paper, Mahler proves that \( {a_n\} \) is a -adic null sequence, and that for all . Thus, can be approximated by polynomials. Mahler goes on to study conditions on the under which is differentiable at a point or has a continuous derivative everywhere on .

Reprint of the author's papers [J. Reine Angew. Math. 199, 23--34 (1958; Zbl 0080.03504); ibid. 208, 70--72 (1961; Zbl 0100.04003)].