Upper bounds for uniform Lebesgue constants of interpolation periodic sourcewise representable splines (Q1675330)

One of the central questions in the approximation of functions especially by interpolation is estimating the size of the Lebesgue number of the (interpolation) operator. In this paper, this question is addressed in great detail in the context of \(2\pi\)-periodic functions. Furthermore, this is specialised to the case of periodic splines, that is we interpolate by a unique \(2\pi\)-periodic spline function whose existence is shown under suitable conditions in an earlier paper by Shevaldin. Here, upper bounds on the Lebesgue numbers of these interpolation operators are provided, as well as examples for the usefulness of the authors' results.