赫-威密度
Hirschman-Widder densities
摘要：
Hirschman和Widder引入了一类由单侧指数函数的线性组合给出的Pólya频率函数。该类的成员是概率密度，并且该类在卷积下是封闭的，但在逐点相乘下不是。我们表明，一般来说，一个多项式函数这样的密度是一个波利亚频率函数，只有当多项式是一个homothety，也确定一个子类，每个正整数功率是波利亚频率函数。我们进一步证明了麦克劳林系数之间的连接，这些密度的时刻，和恢复的密度从100多个时刻，通过舒尔多项式。
英文摘要：
Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations of one-sided exponential functions. The members of this class are probability densities, and the class is closed under convolution but not under pointwise multiplication. We show that, generically, a polynomial function of such a density is a Pólya frequency function only if the polynomial is a homothety, and also identify a subclass for which each positive-integer power is a Pólya frequency function. We further demonstrate connections between the Maclaurin coefficients, the moments of these densities, and the recovery of the density from finitely many moments, via Schur polynomials.
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