New results on regularity and errors of harmonic interpolation using Radon projections
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I. Georgieva [1] ; C. Hofreither [2]
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[1] Bulgarian Academy of Sciences
Bulgarian Academy of Sciences
Bulgaria
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[2] Johannes Kepler University of Linz
Johannes Kepler University of Linz
Linz, Austria
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 293, Nº 1 (February 2016), 2016, págs. 73-81
- Idioma: inglés
- DOI: 10.1016/j.cam.2015.02.056
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Resumen
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.
