We introduce a definition of free multivariate splines which generalizes the univariate notion of splines with free knots. We then concentrate on the simplest case, piecewise constant functions and characterize some classes of functions which have a prescribed order of approximation inL p by these splines. These characterizations involve the classical Besov spaces.
Key words and phrasesMultivariate approximation Splines with free knots Order of approximation Besov spaces
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