A family of interpolation processes is introduced using two positive integral parameters: b a base and 2N an even number of moving nodes. Given y(n), n integer, the authors define , (r integer, as the value of an interpolating Lagrange polynomial; the construction is iterated setting the p’s being finitely many parameters, j integer. An extension y(t) is thus obtained for the set of b-adic rational numbers.
To obtain the properties of the process an associate function F(t) is defined satisfying the functional equation The analysis of F(t) involves the trigonometric polynomials and the infinite matrix: . F(t) is a continuous positive definite function; its order of regularity is precised. The function y(t) is defined as and is proved to be uniformly continuous on any finite interval for all b, N and y(n). Error bounds and examples are given.