Abstract
In this paper we give a definition for differentiation of complex-valued functions defined on a field IK of p-adic or p-series numbers, both in the pointwise and in the strong sense. We show that the characters of IK are eigenvectors of the differentiation operator and that the strong differentiation operator on L1(IK) is a closed operator. Finally we present saturation and non-optimal approximation results for the operators which define the strong L1(IK) derivative.
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References
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© 1978 Birkhäuser Verlag Basel
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Onneweer, C.W. (1978). Differentiation on a p-Adic Or p-Series Field. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_17
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DOI: https://doi.org/10.1007/978-3-0348-7180-8_17
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-0979-4
Online ISBN: 978-3-0348-7180-8
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