Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone

Jacek Wesołowski

Studia Mathematica (2007)

  • Volume: 179, Issue: 3, page 263-275
  • ISSN: 0039-3223

Abstract

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It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.

How to cite

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Jacek Wesołowski. "Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone." Studia Mathematica 179.3 (2007): 263-275. <http://eudml.org/doc/284864>.

@article{JacekWesołowski2007,
abstract = {It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.},
author = {Jacek Wesołowski},
journal = {Studia Mathematica},
keywords = {functional equations; generalized power functions; Lorentz cone; determinant; relativity theory; gamma distribution; Jordan product},
language = {eng},
number = {3},
pages = {263-275},
title = {Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone},
url = {http://eudml.org/doc/284864},
volume = {179},
year = {2007},
}

TY - JOUR
AU - Jacek Wesołowski
TI - Multiplicative Cauchy functional equation and the equation of ratios on the Lorentz cone
JO - Studia Mathematica
PY - 2007
VL - 179
IS - 3
SP - 263
EP - 275
AB - It is proved that the solution of the multiplicative Cauchy functional equation on the Lorentz cone of dimension greater than two is a power function of the determinant. The equation is solved in full generality, i.e. no smoothness assumptions on the unknown function are imposed. Also the functional equation of ratios, of a similar nature, is solved in full generality.
LA - eng
KW - functional equations; generalized power functions; Lorentz cone; determinant; relativity theory; gamma distribution; Jordan product
UR - http://eudml.org/doc/284864
ER -

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