Trigonometric interpolation of function and derivative data

Given the data ƒ(l)}(xp); p = 1,…, m; l = 0,…, np − 1, the periodic functions ƒ(x) are required that have these data as samples, possess a given period and minimal bandwidth, and are in the form of a linear combination of pointwise orthogonal reconstruction functions. For an odd number Σnp of data the unique solution is determined and for an even number, a unique “principal” interpolation function, characterized by minimal highest frequency amplitude of the reconstruction functions. Special consideration is accorded to equidistant data.The problem is related to Gauss's trigonometric interpolation as is Hermite's polynomial interpolation to that of Lagrange