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On the Aleksandrov problem of conservative distances

Authors: Bogdan Mielnik and Themistocles M. Rassias
Journal: Proc. Amer. Math. Soc. 116 (1992), 1115-1118
MSC: Primary 51K05
MathSciNet review: 1101989
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Abstract: A case of the Aleksandrov problem for unit distance preserving mappings between metric spaces is solved. The relevance of methods used in mathematical foundations of quantum mechanics is shown for another case of Aleksandrov problem involving angular distances $ \pi /2$ on the unit sphere.

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  • [1] A. V. Kuz'minyh, On a characteristic property of isometric mappings, Soviet Math. Dokl. 17 (1976), 45-47.
  • [2] F. S. Beckman and D. A. Quarles, On isometries of Euclidean spaces, Proc. Amer. Math. Soc. 4 (1953), 810-815. MR 0058193 (15:335a)
  • [3] Th. M. Rassias, Some remarks on isometric mappings, Facta Univ., Ser. Math. Inform. 2 (1987), 49-52; Report of the 27th Functional Equations Meeting in Bielsko-Bia[unk]a, Poland, August 1989, Aequationes Math. 39 (1990), 304. MR 963783 (89m:51028)
  • [4] B. Mielnik, Phenomenon of mobility in non-linear theories, Commun. Math. Phys. 101 (1985), 323-339. MR 815188 (87b:81013)
  • [5] C. S. Sharma and D. F. Almeida, A direct proof of Wigner's theorem on maps which preserve probabilities between pure states of Quantum systems, Ann. Phys. 197 (1990), 300-309. MR 1036085 (91a:81007)
  • [6] A. M. Gleason, Measures on closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 885-893. MR 0096113 (20:2609)
  • [7] E. P. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. of Math. (2) 40 (1939), 149-204. MR 1503456

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