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Metric transformations of ℝ intoHn

✍ Scribed by Daryl Tingley

Publisher
Springer
Year
1984
Tongue
English
Weight
403 KB
Volume
16
Category
Article
ISSN
0046-5755

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✦ Synopsis

A metric transformation between two metric spaces M 1 and M 2 is defined to be a function f such that for some function p:~+ ~ ~+, called the scale function associated with f, p(dl(x, y)) = dz(f(x), f(y)), for all x, y~M 1 .

Here E+ = {t~lt >~ 0} and neither of the functions f or p is assumed to be continuous.

In a 1938 paper, yon Neumann and Schoenberg [-3] classified all scale functions p associated with continuous metric transformations f from (the real line) to general Hilbert space. In [6] we classified all metric transformations of R into E", including those which are discontinuous. The following was shown.

📜 SIMILAR VOLUMES

Proper gromov transforms of metrics are
Proper gromov transforms of metrics are metrics
✍ A. Dress 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 312 KB

In phylogenetic analysis, a standard problem is to approximate a given metric by an additive metric. Here it is shown that, given a metric D defined on some finite set X and a nonexpansive map f : X + R, the one-parameter family of the Gromov transforms DApf of D relative to f and A that starts with