论文标题
B型的加权手段，分裂差异的阳性和完整的同质对称多项式
Weighted Means of B-Splines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials
论文作者
论文摘要
我们采用了某些分裂差异的事实可以写成为B型的加权手段，因此是积极的。这些划分的差异包括均匀度$ 2p $的完整均质对称多项式，其积极性是D. B. Hunter的经典结果。我们将猎人的结果扩展到完整的分数程度的均匀对称多项式，这些多项式是通过Jacobi的双端公式定义的。我们特别表明，这些多项式对实际程度$μ$具有$ |μ-2P | <1/2 $的真实部分。我们还证明了经典完整同质对称多项式的线性组合的阳性标准，以及对于此类多项式产品的线性组合的阳性的足够标准。
We employ the fact certain divided differences can be written as weighted means of B-splines and hence are positive. These divided differences include the complete homogeneous symmetric polynomials of even degree $2p$, the positivity of which is a classical result by D. B. Hunter. We extend Hunter's result to complete homogeneous symmetric polynomials of fractional degree, which are defined via Jacobi's bialternant formula. We show in particular that these polynomials have positive real part for real degrees $μ$ with $|μ-2p|< 1/2$. We also prove a positivity criterion for linear combinations of the classical complete homogeneous symmetric polynomials and a sufficient criterion for the positivity of linear combinations of products of such polynomials.
