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Abstract. Let $\th\in H^\i $ be an inner function with two spectral points on the unit circle $\T $, and let us consider the numerical range $W(S(\th ))$ of the truncated shift $S(\th )$. The question, whether the shape of $W(S(\th ))$ determines $\th $, is studied. Several conditions are given, when this is true, reducing the problem to a particular case.
DOI: 10.14232/actasm-016-052-0
AMS Subject Classification
(1991): 30H15, 30J05, 47A12, 47A20
Keyword(s):
numerical range,
truncated shift,
inner function,
Herglotz class
Received September 22, 2016, and in revised form March 4, 2017. (Registered under 52/2016.)
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