Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775149 | Journal of Mathematical Analysis and Applications | 2017 | 34 Pages |
Abstract
LetÎ=def{(z+w,zw):|z|â¤1,|w|â¤1}âC2. A Î-inner function is a holomorphic map h from the unit disc D to Î whose boundary values at almost all points of the unit circle T belong to the distinguished boundary bÎ of Î. A rational Î-inner function h induces a continuous map h|T from T to bÎ. 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 Î-inner function of degree n then s2â4p has exactly n zeros in the closed unit disc Dâ, 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 Î-inner functions of degree n with the n zeros of s2â4p prescribed.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jim Agler, Zinaida A. Lykova, N.J. Young,