We introduce a new class of entire functions [Formula: see text] which consists of all [Formula: see text] for which there exists a sequence [Formula: see text] and a sequence [Formula: see text] satisfying [Formula: see text] for all [Formula: see text]. This new class is closed under the composition and it is dense in the space of all nonvanishing entire functions. We prove that every closed set [Formula: see text] containing the origin and at least one more point is the set of singular values of some locally univalent function in [Formula: see text], hence, this new class has nontrivial intersection with both the Speiser class and the Eremenko–Lyubich class of entire functions. As a consequence, we provide a new proof of an old result by Heins which states that every closed set [Formula: see text] is the set of singular values of some locally univalent entire function. The novelty of our construction is that these functions are obtained as a uniform limit of a sequence of entire functions, the process under which the set of singular values is not stable. Finally, we show that the class [Formula: see text] contains functions with an empty Fatou set and also functions whose Fatou set is nonempty.

中文翻译：

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具有规定奇异值的整个函数

我们引入了一个新的全函数类 [Formula: see text]，它由所有 [Formula: see text] 组成，其中存在一个序列 [Formula: see text] 和一个满足 [Formula: see text] 的序列 [Formula: see text] text] 为所有 [公式：见文本]。这个新类在合成下是封闭的，它在所有不消失的整个函数的空间中是密集的。我们证明了每个包含原点和至少一个点的闭集[公式：见文本]是[公式：见文本]中某个局部单价函数的奇异值的集合，因此，这个新类与两者都有非平凡的交​​集整个函数的 Speiser 类和 Eremenko-Lyubich 类。因此，我们为 Heins 的旧结果提供了新证明，该证明指出每个闭集 [公式：见文本] 是一些局部单价整个函数的奇异值的集合。我们构造的新颖之处在于，这些函数是作为一系列完整函数的统一极限获得的，在这个过程中奇异值的集合是不稳定的。最后，我们展示了类 [Formula: see text] 包含具有空 Fatou 集的函数以及 Fatou 集非空的函数。