We solve Cauchy problems for discrete holomorphic functions defined on the Gaussian integers, which leads to the existence of discrete holomorphic functions with arbitrarily fast growth. This proves that certain classes of functions are closed in the sense of mathematical morphology.

中文翻译：

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离散全纯函数的柯西问题

我们针对高斯整数上定义的离散全纯函数解决了柯西问题，从而导致了任意快速增长的离散全纯函数的存在。这证明了某些功能类别在数学形态学意义上是封闭的。