Restricted nonlinear approximation and singular solutions of boundary integral equations

Research output: Journal contributionsJournal articlesResearchpeer-review


This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besov spaces B 6r,r (0.1) with 0<σ<∞ and (1+σ)−1<r<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
Original languageEnglish
JournalApproximation Theory and Its Applications
Issue number1
Pages (from-to)1-25
Number of pages25
Publication statusPublished - 2002