论文标题
钟形序列
Bell-shaped sequences
论文作者
论文摘要
A nonnegative real function $f$ is said to be bell-shaped if it converges to zero at $\pm\infty$ and the $n$th derivative of $f$ changes sign $n$ times for every $n = 0, 1, 2, \ldots$ In a similar way, we may say that a nonnegative sequence $a_k$ is bell-shaped if it converges to zero and the $n$th iterated difference of $a_k$每$ n = 0、1、2，\ ldots $ bell形功能的更改标志$ n $ times最近由托马斯·西蒙（Thomas Simon）和第一作者表征。在本文中，我们提供了对钟形序列的类似描述。更确切地说，我们鉴定出具有Pólya频率序列和完全单调序列的卷积的钟形序列，并且将相应的生成函数表征为适当的挑选函数的指数。
A nonnegative real function $f$ is said to be bell-shaped if it converges to zero at $\pm\infty$ and the $n$th derivative of $f$ changes sign $n$ times for every $n = 0, 1, 2, \ldots$ In a similar way, we may say that a nonnegative sequence $a_k$ is bell-shaped if it converges to zero and the $n$th iterated difference of $a_k$ changes sign $n$ times for every $n = 0, 1, 2, \ldots$ Bell-shaped functions were recently characterised by Thomas Simon and the first author. In the present paper we provide an analogous description of bell-shaped sequences. More precisely, we identify bell-shaped sequences with convolutions of Pólya frequency sequences and completely monotone sequences, and we characterise the corresponding generating functions as exponentials of appropriate Pick functions.
