Overconvergence of Chebyshev and Legendre expansions in quaternionic ellipsoids

DOI10.1007/s00006-015-0554-9zbMath1369.30056OpenAlexW311755650MaRDI QIDQ2361023

Irene Sabadini, Sorin Gheorghe Gal

Publication date: 29 June 2017

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-015-0554-9

zbMATH Keywords

approximationslice regular functionsexpansions in quaternionic ellipsoids

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Approximations and expansions (41A99)

Cites Work

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• Voronovskaja-type results in compact disks for quaternion \(q\)-Bernstein operators, \(q\geq 1\)
• Approximation in compact balls by convolution operators of quaternion and paravector variable
• Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
• Approximation by quaternion \(q\)-Bernstein polynomials, \(q > 1\)
• Carleman type approximation theorem in the quaternionic setting and applications
• Arakelian's approximation theorem of Runge type in the hypercomplex setting
• Regular Functions of a Quaternionic Variable
• Walsh equiconvergence theorems in the quaternionic setting
• The Runge theorem for slice hyperholomorphic functions
• Approximation by polynomials on quaternionic compact sets
• Some remarks on the 𝒮-spectrum
• Universality properties of the quaternionic power series and entire functions

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