Construction of functions from their values at the binary-rational points of an m-dimensional cube
type: Item
instance of: scholarly article
title: Construction of functions from their values at the binary-rational points of an m-dimensional cube
zbMATH Open document ID: 0706.42020
DOI: 10.1007/BF01159260
author: A. S. Shvedov
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: This paper contains the results published by the author in a preprint (No.92/1986) edited by M. V. Keldysh Institute of Applied Mathematics of the Academy of Sciences of the USSR, entitled ``A basis of the space \(C(I^ m)''\). (I denotes the segment [0,1].) The author looks for a basis of the space \(C(I^ m)\), the space of continuous functions on \(I^ m\) in order to study the multidimensional variants of the following problems formulated for the one-dimensional case. ``Let D be the set of binary rational numbers of the segment \(I=[0,1]\). A continuous function f: \(I\to {\mathbb{R}}\) is uniquely defined by its values on the set D. But how do we find out if a function, defined on D, is the trace of a continuous function f: \(I\to {\mathbb{R}}?\) What can be said in this case about the smoothness of the function f? Sufficient conditions for the continuity and the Lipschitz property of a function f (constructively verifiable in concrete situations) can be obtained by making use of the expansion of the function with respect to the Faber-Schauder basis.''
Mathematics Subject Classification ID: 42C30
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 4159365
zbMATH Keywords: Lipschitz property
zbMATH Keywords: Faber-Schauder basis
MaRDI profile type: Publication
cites work: On Schauder Bases for Spaces of Continuous Functions1)
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description: scientific article; zbMATH DE number 4159365