Examples are given of continuous operators of functions analytic on the unit disk having the monomials as eigenvectors which fail spectral synthesis (that is, which have closed invariant subspaces which are not the closed linear span of collections of eigenvectors). Examples include the diagonal operator having as eigenvalues an enumeration of Z x iZ equivalent to {m+in : m, n is an element of Z} and diagonal operators having as eigenvalues enumerations of {n(1/P)e(2 pi ij/3P) : 0 <= j < p} where p is an integer at least 2.
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机译：给出了在具有单项式作为特征向量的单元盘上进行分析的函数的连续算子的示例，这些特征向量使频谱合成失败（也就是说，具有封闭的不变子空间，该子空间不是特征向量集合的封闭线性跨度）。例子包括对角线算子的特征值是Z x iZ的枚举等于{m + in：m，n是Z的元素}和对角线算子的特征值是{n（1 / P）e（2 pi ij / 3P）：0 <= j }，其中p是至少2的整数。
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