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Journal d'Analyse Mathématique

, Volume 134, Issue 1, pp 127–138 | Cite as

Extremal solutions of Nevanlinna-Pick problems and certain classes of inner functions

  • Nacho Monreal Galán
  • Artur Nicolau
Article
  • 35 Downloads

Abstract

Consider a scaled Nevanlinna-Pick interpolation problem and let ∏ be the Blaschke product whose zeros are the nodes of the problem. It is proved that if ∏ belongs to a certain class of inner functions, then the extremal solutions of the problem or most of them are in the same class. Three different classical classes are considered: inner functions whose derivative is in a certain Hardy space, exponential Blaschke products and the well-known class of α-Blaschke products, for 0 < α < 1.

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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Crete, Voutes CampusHeraklion, CreteGreece
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

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