Approximation of harmonic functions by universal overconvergent series » książka
Approximation of harmonic functions by universal overconvergent series
ISBN-13: 9783838366692 / Angielski / Miękka / 2010 / 56 str.
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).
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 Mergelyans 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).
Czytaj nas na:
KrainaKsiazek.PL - Księgarnia Internetowa
