Approximation of harmonic functions by universal overconvergent series - Tamptse, Innocent
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We study the approximation of harmonic functions by universal overconvergent series. Most of the results established are analogues of those obtained in the case of approximation of holomorphic functions by such series. In the case of holomorphic functions, the approximation is made for functions which are continuous on a compact set and holomorphic inside this compact set, while our approximation is for functions that are harmonic in a neighborhood of the compact set. This difference is due to the fact that in the case of holomorphic functions, we have at our disposal Mergelyan's approximation…mehr

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Produktbeschreibung
We study the approximation of harmonic functions by universal overconvergent series. Most of the results established are analogues of those obtained in the case of approximation of holomorphic functions by such series. In the case of holomorphic functions, the approximation is made for functions which are continuous on a compact set and holomorphic inside this compact set, while our approximation is for functions that are harmonic in a neighborhood of the compact set. This difference is due to the fact that in the case of holomorphic functions, we have at our disposal Mergelyan's approximation theorem, which allows such an approximation, while in the case of harmonic functions, we employ only the classic approximation theorem of Walsh (harmonic analogue of the theorem of Runge).
Autorenporträt
Born at Nkongsamba, Cameroon, I begin my university studies at The University of Yaoundé 1, where I obtain a BA, a MA and a DEA in mathematics and then I did my doctorate studies at University of Montréal in Québec, which decerne me a Ph.D of mathematics in 2008. My field of studies concern universal approximation of harmonic functions.