In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x (d))=x 2k 1 1…x 2k d d on S d-1. We obtain the explicit formula on a basis of the orthogonal homogen...In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x (d))=x 2k 1 1…x 2k d d on S d-1. We obtain the explicit formula on a basis of the orthogonal homogeneous polynomials of degree n. It is simpler than the formula in [2], and can be regarded as an extension of [1] under the weighted case.展开更多
In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
基金Supported by the National Natural Science Foundation of China( No. 1 0 2 71 0 2 2 ,and the NaturalScience Foundation of Guangdong Province,China( No.0 2 1 75 5 )
文摘In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x (d))=x 2k 1 1…x 2k d d on S d-1. We obtain the explicit formula on a basis of the orthogonal homogeneous polynomials of degree n. It is simpler than the formula in [2], and can be regarded as an extension of [1] under the weighted case.
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
