The Structure of W-System over Triangular Domains and its Application

W-system on L₂0,1 is a kind of hybrid orthogonal function system constructed by untilizing Haar function and Legendre polynomials.In this paper,we extend the one-dimensional W-system to the case of two variables.The proposed 2D W-system over triangular domain is recursively constructed with Haar matrix and a group of orthonormal bivariate polynomials,using the squeezing,shifting and duplicating methods.The constructed hybrid orthogonal function system is composed of both continuous functions and functions with jumps.It turns out that the new function system is equivalent to the V-system over triangular domain,but its construction process is much simpler.Finally this paper shows that the orthogonal decomposition of a surface group can be realized by the proposed orthogonal function system,and the surface group can be perfectly reconstructed with the obtained frequency spectra.