ON THE NORM OF A COMPOSITION OPERATOR WITH LINEAR FRACTIONAL SYMBOL
ON THE NORM OF A COMPOSITION OPERATOR WITH LINEAR FRACTIONAL SYMBOL
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发表时间：
2003
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通讯作者：
Christopher N. B. Hammond;Barbara D. Maccluer
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作者：
Christopher N. B. Hammond;Barbara D. Maccluer
对于任意解析映射φ: D→D，复合算子Cφ在Hardy空间H2上是有界的，但没有已知的精确计算其范数的方法。本文考虑φ是一个线性分数映射的情况。我们通过Cφ或C * φ对H2的归一化再生核函数的作用确定了‖Cφ‖是给定的条件。我们还在φ上引入了一组新的条件，在这些条件下我们可以计算‖Cφ‖；此外，我们还确定了H2中使算子Cφ达到范数的元素。提供了几个具体的例子。
For any analytic map φ : D→ D, the composition operator Cφ is bounded on the Hardy space H2, but there is no known procedure for precisely computing its norm. This paper considers the situation where φ is a linear fractional map. We determine the conditions under which ‖Cφ‖ is given by the action of either Cφ or C∗ φ on the normalized reproducing kernel functions of H2. We also introduce a new set of conditions on φ under which we can calculate ‖Cφ‖; moreover, we identify the elements of H2 on which such an operator Cφ attains its norm. Several specific examples are provided.