A derivative on the field of \(p\)-adic numbers
type: Item
instance of: scholarly article
title: A derivative on the field of \(p\)-adic numbers
zbMATH Open document ID: 1284.46065
DOI: 10.1134/S2070046610040023
published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
publication date: 2012-11-13T00:00:00Z
review text: The authors introduce a new pointwise \(p\)-adic derivative for complex-valued locally constant functions defined on the field \(\mathbb{Q}_p\) of \(p\)-adic numbers, and investigate some basic properties of this derivative (\(p\) is a prime number). They study the derivative of a regular distribution and of the multiplicative convolution, as well as the derivative of the Fourier transform. Among other things, they prove that the Fourier transform of any locally constant function with compact support is infinitely differentiable. The results obtained in this paper provide a partial answer to the problem posed in [\textit{W.-Y. Su} and \textit{H. Qiu}, ``\(p\)-adic calculus and its applications to fractal analysis and medical science'', Facta Univ., Ser. Electron. Energ. 21, No. 3, 339--347 (2008; \url{doi:10.2298/FUEE0803339S})] of developing \(p\)-adic calculus on the multiplicative group of a \(p\)-adic field.
reviewed by: Cristina Pérez-García
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 26E30
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 6105052
zbMATH Keywords: \(p\)-adic derivative
zbMATH Keywords: homogeneous distributions
zbMATH Keywords: multiplicative convolution
Wikidata QID: Q57621849
author: Muharem Avdispahić
author: N. Memić
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6105052