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On the construction of uniformly convergent disk polynomial expansions

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An Erratum to this article was published on 15 May 2012

Abstract

We present a method to derive explicit uniformly convergent disk polynomial expansions for real-analytic functions on the complex unit disk. As an application, we deduce the spherical harmonic expansion of the Poisson–Szegö kernel for the unit ball in \({\mathbb{C}^q}\) .

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Authors and Affiliations

  1. Departamento de Matemática, ICMC-USP, São Carlos, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil

    V. A. Menegatto & A. P. Peron

  2. Universidade Federal de Itajubá, ICE-DMC, Caixa Postal 50, 37500-903, Itajubá, MG, Brazil

    C. P. Oliveira

Authors
  1. V. A. Menegatto
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  2. A. P. Peron
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  3. C. P. Oliveira
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Corresponding author

Correspondence to V. A. Menegatto.

Additional information

This work had a financial support from FAPEMIG, Grant # APQ-01261-08. A. P. Peron’s work was partially supported by FAPESP, Brazil, Grant # 08/54221-0.

An erratum to this article can be found at http://dx.doi.org/10.1007/s13348-012-0064-1

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Menegatto, V.A., Peron, A.P. & Oliveira, C.P. On the construction of uniformly convergent disk polynomial expansions. Collect. Math. 62, 151–159 (2011). https://doi.org/10.1007/s13348-010-0017-5

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  • DOI: https://doi.org/10.1007/s13348-010-0017-5

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