Radial Triangular Lagrange Interpolation

In this paper,we mainly discuss the problem of the trigonometric function interpolation spaces , the radial trigonometric Lagrange interpolaton formula on S1 and the Cartisan trigonometric Lagrange interpolation formula on S2 .Four section are included in this paper.In section l,the introduction is included. We introduce the problem of multivariate interpolation and trigonometric interpolaton .Also the concepts of continuous function on S1 or S2 and polynomial and trigonometric function under polar coordinates are introduced. In secton 2, we introduce some different trigonometric interpolation function spaces and their relations, which is the basis of the following discussion. In secion 3, we give the radial trigonometric Lagrange interpolation formula on S1 according to different interpolation spaces and the Cartisan trigonometric Lagrange interpolation formula on S2 . In secion 4,we draw some examples of trigonometric Lagrange interpolation on S1 and S2.The radial trigonometric Lagrange interpolation on S1and S2 prepares for the further appliation on periodic function, numerical intergration formula and finite element etc.