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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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