A conjectured class of scale-invariant distances on inner product spaces

Bruno Galvan

A conjectured class of scale-invariant distances on inner product spaces

Quantum Physics 2014-01-10 v2 Mathematical Physics Functional Analysis math.MP

Authors: Bruno Galvan

Abstract

Let $V$ be an inner product space, and $x, y \in V$ ; the conjecture is made that, for any $p \in [1, \infty]$ , the function $d_p(x, y):=\|x-y\|/(\|x\|^p+ \|y\|^p)^{1/p}$ is a distance on $V$ .

Keywords

scale-invariant distance inner product space metric space conjecture norm inequality

Cite

@article{arxiv.1401.1524,
  title  = {A conjectured class of scale-invariant distances on inner product spaces},
  author = {Bruno Galvan},
  journal= {arXiv preprint arXiv:1401.1524},
  year   = {2014}
}

Comments

This paper has been withdrawn by the author. The conjecture was already been made and solved. See Peter A. H\"ast\"o, A new weighted metric: the relative metric I, J. Math. Anal. Appl. 274, 38-58 (2002). Thanks to prof. Heinz Bauschke

A conjectured class of scale-invariant distances on inner product spaces

Abstract

Keywords

Cite

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