Strict p-negative type of a metric space

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Strict p-negative type of a metric space

Doust and Weston (J Funct Anal 254:2336–2364, 2008) have introduced a new method called enhanced negative type for calculating a non-trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be nontrivial. In this paper we refine the technique of enhanced negative type and ...

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STRICT p-NEGATIVE TYPE OF A SEMI-METRIC SPACE

Doust and Weston [8] introduced a new method called “enhanced negative type” for calculating a non trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). (In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be non trivial.) In this paper we refine the technique of enhanced negative type and show how it may be applied more...

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THE SUPREMAL p-NEGATIVE TYPE OF A FINITE SEMI-METRIC SPACE CANNOT BE STRICT

Doust and Weston [5] introduced a new method called “enhanced negative type” for calculating a non trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T, d). (In the context of finite metric trees any such lower bound ℘T > 1 is deemed to be non trivial.) In this paper we refine the technique of enhanced negative type and show how it may be applied more...

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OPTIMAL LOWER BOUND ON THE SUPREMAL STRICT p-NEGATIVE TYPE OF A FINITE METRIC SPACE

Determining meaningful lower bounds on the supremal strict p-negative type of classes of finite metric spaces is a difficult nonlinear problem. In this paper we use an elementary approach to obtain the following result: given a finite metric space (X, d) there is a constant ζ > 0, dependent only on n = |X | and the scaled diameter D= (diam X)/min{d(x, y) | x 6= y} of X (which we may assume is >...

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ژورنال

عنوان ژورنال: Positivity

سال: 2009

ISSN: 1385-1292,1572-9281

DOI: 10.1007/s11117-009-0035-2