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Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 125–133 | Cite as

Overconvergence of Chebyshev and Legendre Expansions in Quaternionic Ellipsoids

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Abstract

In this paper we show that for any slice regular function f in a quaternionic ellipsoid containing their real interval of orthogonality, the Chebyshev and Legendre expansions converge uniformly to f in all compact subsets in the interior of the ellipsoid, with the order of a geometric series.

Keywords

Chebyshev and Legendre polynomials Slice regular functions Expansions in quaternionic ellipsoids 

Mathematics Subject Classification

Primary 30G35 Secondary 30E10 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of OradeaOradeaRomania
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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