Geodesic
Extremal functions of the Nevanlinna-Pick problem and Douglas algebras
Studia Mathematica, Tome 105 (1993) no. 2, pp. 151-158

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The Nevanlinna-Pick problem at the zeros of a Blaschke product B having a solution of norm smaller than one is studied. All its extremal solutions are invertible in the Douglas algebra D generated by B. If B is a finite product of sparse Blaschke products (Newman Blaschke products, Frostman Blaschke products) then so are all the extremal solutions. For a Blaschke product B a formula is given for the number C(B) such that if the NP-problem has a solution of norm smaller than C(B) then all its extremal solutions are Carleson Blaschke products, i.e. can be represented as finite products of interpolating Blaschke products.
DOI : 10.4064/sm-105-2-151-158

V. Tolokonnikov 1

1 
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V. Tolokonnikov. Extremal functions of the Nevanlinna-Pick problem and Douglas algebras. Studia Mathematica, Tome 105 (1993) no. 2, pp. 151-158. doi: 10.4064/sm-105-2-151-158

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