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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Oradea, Str. Universitatii Nr. 1, 410087, Oradea, Romania

    Sorin G. Gal

  2. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133, Milano, Italy

    Irene Sabadini

Authors
  1. Sorin G. Gal
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  2. Irene Sabadini
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Correspondence to Irene Sabadini.

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Gal, S.G., Sabadini, I. Overconvergence of Chebyshev and Legendre Expansions in Quaternionic Ellipsoids. Adv. Appl. Clifford Algebras 27, 125–133 (2017). https://doi.org/10.1007/s00006-015-0554-9

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  • DOI: https://doi.org/10.1007/s00006-015-0554-9

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