Quasi-interpolants based on trigonometric splines. (English) Zbl 0912.41008

In this paper the authors develop a general theory of quasi-interpolants based on trigonometric splines. Although the analysis is parallel to the familiar treatment of quasi-interpolants based on polynomial splines, the details are complicated because of the nature of trigonometric splines. In addition to developing a general theory they give an detailed treatment of two interesting classes of quasi-interpolants based on derivative formation and on simple point evaluation. The authors provide some general remarks as to how further studies in related fields can be carried on.


41A15 Spline approximation
41A30 Approximation by other special function classes
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