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This paper considers the extension of classical Lagrange interpolation in onereal or complex variable to "polynomials of one quaternionic variable". To dothis we develop some aspects of the theory of such polynomials. We then give anumber of related multivariate polynomial interpolation schemes for${\mathbb{R}}^4$ and ${\mathbb{C}}^2$ with good geometric properties, and someaspects of least interpolation and of Kergin interpolation.

Multivariate Lagrange interpolation and polynomials of one quaternionic variable