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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The first author is also supported by the research project PE1(3378) implemented within the framework of the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), cofinanced by the European Social Fund (ESF) and the Greek State.
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Galán, N.M., Nicolau, A. Extremal solutions of Nevanlinna-Pick problems and certain classes of inner functions. JAMA 134, 127–138 (2018). https://doi.org/10.1007/s11854-018-0004-4
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DOI: https://doi.org/10.1007/s11854-018-0004-4