Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898221 | Applied and Computational Harmonic Analysis | 2018 | 27 Pages |
Abstract
The main contributions of this paper, however, are the generalizations of the aforementioned results to the setting of the product of two or more tree metric spaces. For functions on a product space, the notion of regularity we consider is not the Lipschitz condition, but rather the mixed Lipschitz condition that controls the size of a function's mixed difference quotient. This condition is extremely natural for datasets that can be described as a product of metric spaces, such as word-document databases. We develop effective formulas for norms equivalent to the mixed Lipschitz norm and its dual, and extend our results on combining pairs of trees.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
William Leeb,