New results on regularity and errors of harmonic interpolation using Radon projections

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• 作者：I. Georgieva^a ; ^{irina@math.bas.bg" class="auth_mail" title="E-mail the corresponding author} ; C. Hofreither^b ; ^{chofreither@numa.uni-linz.ac.at" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multivariate interpolation ; Radon projections ; Harmonic polynomials
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：293
• 期：Complete
• 页码：73-81
• 全文大小：553 K

文摘

We study interpolation of harmonic functions in the unit disk with a finite number of values of the Radon projection along prescribed chords as the input data. We seek the interpolant in the space of harmonic polynomials in such a way that it matches the given projection values exactly. In this setting, we investigate schemes where all chords are divided into two sets of parallel chords. We give necessary and sufficient conditions for a scheme of this type to result in a uniquely solvable interpolation problem. As a second new result, we generalize the previously known error estimates for schemes with equispaced chord angles, both to allow for a larger class of chord choices and to obtain new error estimates in fractional Sobolev norms.