涉及缺项序列的强自然边界的充分条件
Sufficient Conditions for Strong Natural Boundaries involving Lacunary Sequences
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中文总结 AI 辅助
该研究将正则点推广为弱正则点，得出强自然边界的充分条件：基础幂级数系数无界且指数构成缺项序列时满足对应间隙密度条件之一。
中文摘要 AI 辅助
正则点的概念被推广为弱正则点，因此强自然边界的概念可局部描述为弱正则点的缺失，正如自然边界局部是正则点的缺失。主要结果是强自然边界的一个充分条件，即基础幂级数的系数无界，且指数满足两个特定间隙密度条件之一，该指数构成缺项序列。
英文摘要
The notion of a regular point is extended to that of a weak regular point, and so the notion of a strong natural boundary may be described locally as the absence of weak regular points, just as a natural boundary is locally the absence of regular points. The main result is a sufficient condition for a strong natural boundary, which is the conjunction of the unboundedness of the coefficients of the underlying power series with either of two specific gap density conditions imposed on the exponents that yields a lacunary sequence.
