A theory of discrete analysis
type: Item
instance of: scholarly article
title: A theory of discrete analysis
zbMATH Open document ID: 0781.46030
DOI: 10.1016/0022-247X(92)90085-R
author: Daniel M. Hyman
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-05-16T00:00:00Z
review text: In a previous paper the author characterized Lipschitz mappings in terms of sequences of finite variation. By using this characterization, in the present paper a discrete analysis is developed which is a purely algebraic construction. The major constructions in discrete analysis are: discrete differential structures, the integral envelope and the integral completion. It is shown that the space of real numbers is the integral completion of rational numbers and the space of all complex periodic distributions is the integral completion of the class of infinitely differentiable periodic functions.
Mathematics Subject Classification ID: 46F99
zbMATH DE Number: 167995
zbMATH Keywords: Lipschitz mappings
zbMATH Keywords: sequences of finite variation
zbMATH Keywords: discrete analysis
zbMATH Keywords: purely algebraic construction
zbMATH Keywords: discrete differential structures
zbMATH Keywords: integral envelope
zbMATH Keywords: integral completion
zbMATH Keywords: complex periodic distributions
reviewed by: László Simon
MaRDI profile type: Publication
cites work: Q5685587
cites work: Q3976350
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description: scientific article; zbMATH DE number 167995