Wolff-Denjoy级数Wiener引理的模拟
Analog for the Wiener Lemma for Wolff-Denjoy Series
摘要：
设函数f为实极点展开的正系数Wolff-Denjoy级数。笔记的主要结果是，如果我们从函数1/f中减去它的线性部分，那么这个函数的剩余分数部分也将扩展为沃尔夫-丹享受级数（它的极点也是实数，级数的系数是负数）。换句话说，对于所示形式的Wolff-Denjoy级数，傅里叶级数理论中著名的维纳引理的类似物在线性项之前是正确的。最后给出了结果在算子理论中的应用.
英文摘要：
Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this function will also expand into Wolff-Denjoy series (its poles are also real, and the coefficients of the series are negative). In other words, for Wolff-Denjoy series of the indicated form, an analogue of the well-known Wiener lemma in the theory of Fourier series is true up to a linear term. Applications of the result to operator theory are given.
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