Optimal Convergence Rates for Tikhonov Regularization in Besov Scales
Functional Analysis
2009-11-13 v2
Abstract
In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vive versa. Moreover, we present optimal source conditions for regularization in Besov scales.
Keywords
Cite
@article{arxiv.0806.0951,
title = {Optimal Convergence Rates for Tikhonov Regularization in Besov Scales},
author = {Dirk Lorenz and Dennis Trede},
journal= {arXiv preprint arXiv:0806.0951},
year = {2009}
}