Piecewise linear bases and Besov spaces on fractal sets
type: Item
instance of: scholarly article
title: Piecewise linear bases and Besov spaces on fractal sets
zbMATH Open document ID: 0994.46009
DOI: 10.1023/A:1014334924583
author: Alf Jonsson
author: Anna Kamont
published in: Analysis Mathematica
publication date: 2002-06-25T00:00:00Z
review text: For a compact d-dimensional fractal subset \(F\) of \({\mathbf R^n}\) endowed with a Hausdorff measure and admitting a convenient sequence of triangulations (a number of examples of such sets are included in the paper), analogues of the Faber--Schauder and of the Franklin systems are described, and several applications to Besov spaces on this fractal set for a certain range of parameters are given. These applications include the construction of extension operators for pairs of sets \(G\subset F\), and the characterization of Besov spaces in terms of coefficients of functions with respect to wavelets bases.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1759076
zbMATH Keywords: Besov space
zbMATH Keywords: fractal set
zbMATH Keywords: wavelet
zbMATH Keywords: Faber-Schauder system
zbMATH Keywords: Franklin system
reviewed by: Joan Cerdà
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1759076