乘子序列与对数网格
Multiplier sequences and logarithmic mesh
摘要：
本文证明了关于（有限）乘子序列的一个新结果，即线性算子在R[x]的标准单项式基上对角作用，使具有全部实根的多项式变为具有全部实根的多项式.也就是说，我们表明，任何这样的运营商不减少对数网格时，作用于一个任意的多项式具有所有的根真正的和相同的符号。这样的多项式的对数网格被定义为以非降阶取的其连续根的最小商。
英文摘要：
In this note we prove a new result about (finite) multiplier sequences, i.e. linear operators acting diagonally in the standard monomial basis of R[x] and sending polynomials with all real roots to polynomials with all real roots. Namely, we show that any such operator does not decrease the logarithmic mesh when acting on an arbitrary polynomial having all roots real and of the same sign. The logarithmic mesh of such a polynomial is defined as the minimal quotient of its consecutive roots taken in the non-decreasing order.
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