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May I suggest that you look at the Annals of Statistics paper "Estimation of a Multivariate Density Function Using Delta Sequences," see if that paper's definition of a multivariate delta sequence matches what you have in mind by your phrase "multidimensional delta sequence," and if so, work forward in time through the 17 more recent papers and books that Google Scholar lists as citing this early paper. Finally, you might consider posting a more detailed version of your question to https://stats.stackexchange.com/.