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Title

Extremal functions of the Nevanlinna-Pick problem and Douglas algebras

Authors 1

Affiliations

  1. Topzhkovskaya St., D.2, Kor. 1, KV. 76, 197342 St. Petersburg, Russia

Abstract

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.

Bibliography

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Studia Mathematica
1993/105/2
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Pages:
151-158
Main language of publication
English
Received
1992-06-30
Published
1993
Exact and natural sciences