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On Two and Three Variables Trigonometric Surfaces and Orthogonal Polynomials Over Some Irregular Domains

Jiachang Sun  
【摘要】:正In this speech based on second order PDE eigen-problems we construct the retionship between trigonometric surface and orthogonal polynomial surface in 2-D and 3-D over some irregular domains The main PDE operator can be seen a mapping of 2-D or 3-D Laplacian from a triable or a tetrahedron domains.Some recunences relations so called three-layer have been found in terms of several terms instead of three terms for univariate case. As three examples,the two and three-variable analogues of the first and second Chebyshev polynomials and Legendre polynomials are discussed.

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