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Advances in Complex Analysis and Operator Theory pp 19–35Cite as

Birkhäuser

Divided Differences and Two-sided Polynomial Interpolation Over Quaternions

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

Abstract

We consider a two-sided interpolation problem of Lagrange–Hermite type for polynomials over quaternions. Necessary and sufficient condition for the problem to have a solution is given and a particular low-degree solution is constructed in terms of a certain Sylvester equation.

Dedicated to Professor Daniel Alpay on the occasion of his 60th birthday

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Author information

Authors and Affiliations

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

    Vladimir Bolotnikov

Authors
  1. Vladimir Bolotnikov
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Correspondence to Vladimir Bolotnikov .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Fabrizio Colombo

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  3. Schmid College of Science and Technology, Chapman University, Orange, California, USA

    Daniele C. Struppa

  4. Schmid College of Science and Technology, Chapman University, Orange, California, USA

    Mihaela B. Vajiac

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Bolotnikov, V. (2017). Divided Differences and Two-sided Polynomial Interpolation Over Quaternions. In: Colombo, F., Sabadini, I., Struppa, D., Vajiac, M. (eds) Advances in Complex Analysis and Operator Theory. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-62362-7_2

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