Lagrange interpolation problem for quaternion polynomials
The classical Lagrange interpolation problem over the field of complex numbers has some relevance in several branches of mathematics. For instance, it is important in approximation theory, numerical analysis and control theory. A generalization over other finite fields will open up further applications. The author considers the Lagrange problem over the skew-field of real quaternions. Left and right problems arise. Algebraical means that solvability criterions are formulated and a solution is derived. It should be mentioned that there exists a paper by \textit{K. Gürlebeck} [Wiss. Inf. 34, 21 S. (1982; Zbl 0551.41004)] which provides a complete construction of a monogenic (i.e., included in the kernel of the Dirac operator) quaternionic (left) Lagrange interpolation polynomial, on the basis of total analytic variables. This result can also be found in the book by \textit{K. Gürlebeck} and the reviewer [Quaternionic analysis and elliptic boundary value problems. Basel: Birkhäuser (1990; Zbl 0850.35001)].
scientific article; zbMATH DE number 6339665
scientific article