Additive combination spaces

Additive combination spaces We introduce a class of metric spaces called $$p$$ p -additive combinations and show that for such spaces we may deduce information about their $$p$$ p -negative type behaviour by focusing on a relatively small collection of almost disjoint metric subspaces, which we call the components. In particular we deduce a formula for the $$p$$ p -negative type gap of the space in terms of the $$p$$ p -negative type gaps of the components, independent of how the components are arranged in the ambient space. This generalizes earlier work on metric trees by Doust and Weston. The results hold for semi-metric spaces as well, as the triangle inequality is not used. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Additive combination spaces

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Publisher
Springer Basel
Copyright
Copyright © 2014 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-014-0304-6
Publisher site
See Article on Publisher Site

Abstract

We introduce a class of metric spaces called $$p$$ p -additive combinations and show that for such spaces we may deduce information about their $$p$$ p -negative type behaviour by focusing on a relatively small collection of almost disjoint metric subspaces, which we call the components. In particular we deduce a formula for the $$p$$ p -negative type gap of the space in terms of the $$p$$ p -negative type gaps of the components, independent of how the components are arranged in the ambient space. This generalizes earlier work on metric trees by Doust and Weston. The results hold for semi-metric spaces as well, as the triangle inequality is not used.

Journal

PositivitySpringer Journals

Published: Aug 20, 2014

References

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