Article ID Journal Published Year Pages File Type
5775149 Journal of Mathematical Analysis and Applications 2017 34 Pages PDF
Abstract
LetΓ=def{(z+w,zw):|z|≤1,|w|≤1}⊂C2. A Γ-inner function is a holomorphic map h from the unit disc D to Γ whose boundary values at almost all points of the unit circle T belong to the distinguished boundary bΓ of Γ. A rational Γ-inner function h induces a continuous map h|T from T to bΓ. The latter set is topologically a Möbius band and so has fundamental group Z. The degree of h is defined to be the topological degree of h|T. In a previous paper the authors showed that if h=(s,p) is a rational Γ-inner function of degree n then s2−4p has exactly n zeros in the closed unit disc D−, counted with an appropriate notion of multiplicity. In this paper, with the aid of a solution of an interpolation problem for finite Blaschke products, we explicitly construct the rational Γ-inner functions of degree n with the n zeros of s2−4p prescribed.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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