Abstract
Let ϑ ∈ H∞ be an inner function with two spectral points on the unit circle T, and let us consider the numerical range W(S(ϑ)) of the truncated shift S(ϑ). The question, whether the shape of W(S(ϑ)) determines ϑ, is studied. Several conditions are given, when this is true, reducing the problem to a particular case.
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Kérchy, L. Uniqueness of the numerical range of truncated shifts. ActaSci.Math. 83, 243–261 (2017). https://doi.org/10.14232/actasm-016-052-0
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DOI: https://doi.org/10.14232/actasm-016-052-0