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Shift operators contained in contractions, pseudocontinuable Schur functions and orthogonal systems on the unit circle

机译:单位圆上的收缩,伪连续Schur函数和正交系统中包含的移位算符

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摘要

The main aim of this paper is to establish the connection between wellknown criteria for the pseudocontinuability of a non-inner Schur function-in the unit disk (see Theorems 3.9, 4.2). In a canonical way we associate a probability measure μ on the unit circle with -. One of the two criteria will be reformulated in the face of μ, whereas the other one is drafted in view of a completely nonunitary contraction T having - as corresponding characteristic function. Our main result clarifies an immediate connection between the above-mentioned two criteria. In this way, we rewrite these criteria in terms of orthogonal systems with respect to the measure μ (see Theorem 7.2).
机译:本文的主要目的是建立单位磁盘中非内部Schur函数的伪连续性的知名标准之间的联系(请参见定理3.9、4.2)。以规范的方式,我们将单位圆上的概率测度μ与-关联。将在μ的面上重新制定两个标准之一,而考虑具有-作为相应特征函数的完全非单位收缩T来拟定另一个标准。我们的主要结果阐明了上述两个标准之间的直接联系。这样,我们根据关于度量μ的正交系统来重写这些标准(请参见定理7.2)。

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