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. 
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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