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Conjugate Jacobi Series and Conjugate Functions

Name: Conjugate Jacobi Series and Conjugate Functions
Creator: Zhongkai Li
Keywords: Mathematics(all), Numerical Analysis, convergence, Applied Mathematics, Abel means, weak-\(L_ 1\) boundedness, 01 natural sciences, conjugate harmonic function, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), conjugate Jacobi series

Conjugate Jacobi series and conjugate functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1996 English Publisher:Elsevier BVJournal:Journal of Approximation Theory, volume 86, pages 179-196 (issn: 0021-9045,

Authors: Zhongkai Li;

doi: 10.1006/jath.1996.0061

Conjugate Jacobi Series and Conjugate Functions

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Abstract

The starting point is the notion of conjugacy on a Euclidean \(n\)-space as defined by \textit{E. M. Stein} and \textit{G. Weiss} [Acta Math. 103, 25-62 (1962; Zbl 0097.28501)]. Conjugate Jacobi series is introduced in the sense that the Jacobi harmonic function and the conjugate harmonic function (indicated in the title) satisfy the generalized Cauchy-Riemann equations. An integral representation of the Jacobi conjugate function is also given, which is identifiable with the conjugate Jacobi series in some sense. The author proves weak-\(L_1\) boundedness and \(L_p\) boundedness properties of the conjugate mapping for \(1

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Capital Normal University
China (People's Republic of)

Keywords

Mathematics(all), Numerical Analysis, convergence, Applied Mathematics, Abel means, weak-\(L_ 1\) boundedness, conjugate harmonic function, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), conjugate Jacobi series, Jacobi harmonic function, Analysis, \(L_ p\) boundedness

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