论文标题
指数和对数长度的光谱合成
Spectral synthesis for exponentials and logarithmic length
论文作者
论文摘要
我们研究指数系统的遗传性完整性，使得相应的生成函数$ g $在间隔$ i_k $的间隔序列外部很小。我们表明，在某些技术条件下，只有当这些间隔的结合的对数长度是无限的，即$ \ sum_k \ int_ {i_k {i_k} \ frac {dx} {1+ | x | x |} = \ infty $。
We study hereditary completeness of systems of exponentials on an interval such that the corresponding generating function $G$ is small outside of a lacunary sequence of intervals $I_k$. We show that, under some technical conditions, an exponential system is hereditarily complete if and only if the logarithmic length of the union of these intervals is infinite, i.e., $\sum_k\int_{I_k} \frac{dx}{1+|x|}=\infty$.
