Closed balls for interpolating quasi-polynomials

the classic interpolation problem asks for polynomials to fit a set of given data. in this paper, quasi-polynomials are considered as interpolating functions passing through a set of spatial points. existence and uniqueness is obtained by means of generalized vandermonde determinants. by means of several estimates related to these determinants, we are also able to find closed balls for any given centers that enclose the approximating curves. by choosing proper centers based on the observed spatial points, these balls may lead us to applications such as satellite tracking and control. mathematical subject classification: 41a05.