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Reproducing kernel Hilbert spaces and fractal interpolation. (English) Zbl 1226.65009

The main result of this work is to link two fields: fractal interpolation and reproducing kernel Hilbert space. The corresponding spaces of the simple fractal interpolation functions are also reproducing kernel Hilbert spaces, as specific cases. The authors provide the elements for calculating the respective kernel functions for reproducing kernel Hilbert spaces and the corresponding induced mappings.

MSC:

65D05 Numerical interpolation
41A30 Approximation by other special function classes
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
41A05 Interpolation in approximation theory
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