On Orthonormal Polynomial Solutions of the Riesz System in ℝ3

K. Gürlebeck () and J. Morais ()
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K. Gürlebeck: Bauhaus-Universität Weimar, Institut für Mathematik/Physik
J. Morais: Bauhaus-Universität Weimar, Institut für Mathematik/Physik

Chapter Chapter 6 in Recent Advances in Computational and Applied Mathematics, 2011, pp 143-158 from Springer

Abstract: Abstract The main goal of the paper is to deal with a special orthogonal system of polynomial solutions of the Riesz system in ℝ3. The restriction to the sphere of this system is analogous to the complex case of the Fourier exponential functions {e in θ } n≥0 on the unit circle and has the additional property that also the scalar parts of the polynomials form an orthogonal system. The properties of the system will be applied to the explicit calculation of conjugate harmonic functions with a certain regularity.

Keywords: Quaternionic analysis; Homogeneous monogenic polynomials; Riesz system; Harmonic conjugates; 30G35; 31B05; 31B35 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-90-481-9981-5_6

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DOI: 10.1007/978-90-481-9981-5_6

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