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

Nacho Monreal Galán; Artur Nicolau

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arXiv · 1405.3578

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

Nacho Monreal Galán·Artur Nicolau

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Abstract

Consider a scaled Nevanlinna-Pick interpolation problem and let $\Pi$ be the Blaschke product whose zeros are the nodes of the problem. It is proved that if $\Pi$ 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 also the well known class of $\alpha$-Blaschke products, for $0<\alpha<1$.

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Nacho Monreal Galán, Artur Nicolau. 2014-05-14. Extremal solutions of Nevalinna-Pick problems and certain classes of inner functions. https://arxiv.org/abs/1405.3578

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