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math.FA2024
On Sobolev and Besov Spaces of Hybrid Regularity
Helmut Harbrecht, Remo von Rickenbach
The present article is concerned with the nonlinear approximation of functions in the Sobolev space H^q with respect to a tensor-product, or hyperbolic wavelet basis on the unit n-…
math.NA2024
On Quasi-Localized Dual Pairs in Reproducing Kernel Hilbert Spaces
Helmut Harbrecht, Rüdiger Kempf, Michael Multerer
In scattered data approximation, the span of a finite number of translates of a chosen radial basis function is used as approximation space and the basis of translates is used for…
math.NA2024
The dimension weighted fast multipole method for scattered data approximation
Helmut Harbrecht, Michael Multerer, Jacopo Quizi
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse p…