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Boundary Interpolation by Finite Blaschke Products

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Book cover Complex Analysis and Dynamical Systems

Part of the book series: Trends in Mathematics ((TM))

Abstract

Given n distinct points t 1, …, t n on the unit circle \({\mathbb T}\) and equally many target values \(w_1,\ldots ,w_n\in {\mathbb T}\), we describe all Blaschke products f of degree at most n − 1 such that f(t i ) = w i for i = 1, …, n. We also describe the cases where degree n − 1 is the minimal possible.

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Authors and Affiliations

  1. Department of Mathematics, The College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov

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  1. Vladimir Bolotnikov
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Correspondence to Vladimir Bolotnikov .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Mark Agranovsky

  2. Department of Mathematics, Holon Institute of Technology, Holon, Israel

    Anatoly Golberg

  3. Department of Mathematics, ORT Braude College, Karmiel, Israel

    Fiana Jacobzon

  4. Department of Mathematics, Holon Institute of Technology, Holon, Israel

    David Shoikhet

  5. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Lawrence Zalcman

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Bolotnikov, V. (2018). Boundary Interpolation by Finite Blaschke Products. In: Agranovsky, M., Golberg, A., Jacobzon, F., Shoikhet, D., Zalcman, L. (eds) Complex Analysis and Dynamical Systems. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70154-7_3

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