Clark measures on the torus

Let D\mathbb {D} denote the unit disc of C\mathbb {C} and let T=∂D\mathbb {T}= \partial \mathbb {D}. Given a holomorphic function φ:Dn→D\varphi : \mathbb {D}^n \to \mathbb {D}, n≥2n\ge 2, we study the corresponding family σα[φ]\sigma _\alpha [\varphi ], α∈T\alpha \in \mathbb {T}, of Clark measures o...

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Veröffentlicht in:	Proceedings of the American Mathematical Society 2020-05, Vol.148 (5), p.2009-2017
1. Verfasser:	Doubtsov, Evgueni
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Sprache:	eng
Schlagworte:	Research article
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description	Let D\mathbb {D} denote the unit disc of C\mathbb {C} and let T=∂D\mathbb {T}= \partial \mathbb {D}. Given a holomorphic function φ:Dn→D\varphi : \mathbb {D}^n \to \mathbb {D}, n≥2n\ge 2, we study the corresponding family σα[φ]\sigma _\alpha [\varphi ], α∈T\alpha \in \mathbb {T}, of Clark measures on the torus Tn\mathbb {T}^n. If φ\varphi is an inner function, then we introduce and investigate related isometric operators TαT_\alpha mapping analogs of model spaces into L2(σα)L^2(\sigma _\alpha ), α∈T\alpha \in \mathbb {T}.
doi_str_mv	10.1090/proc/14846
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title	Clark measures on the torus
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