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
We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded...We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.展开更多
A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the ...A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.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 National Natural Science Foundation of China(Grant No.11071119)
文摘We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.
基金supported by Tian Yuan Foundation of China (10526033)China Postdoctoral Science Foundation (2005038639)the Natural Science Foundation of China (10601040,10571144).
文摘A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.
