On Popoviciu-Ionescu Functional Equation

Jose M. Almira. "On Popoviciu-Ionescu Functional Equation." Annales Mathematicae Silesianae 30.1 (2016): 5-15. <http://eudml.org/doc/286778>.

@article{JoseM2016,
abstract = {We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.},
author = {Jose M. Almira},
journal = {Annales Mathematicae Silesianae},
keywords = {functional equations; exponential polynomials on Abelian groups; Montel type theorem},
language = {eng},
number = {1},
pages = {5-15},
title = {On Popoviciu-Ionescu Functional Equation},
url = {http://eudml.org/doc/286778},
volume = {30},
year = {2016},
}

TY - JOUR
AU - Jose M. Almira
TI - On Popoviciu-Ionescu Functional Equation
JO - Annales Mathematicae Silesianae
PY - 2016
VL - 30
IS - 1
SP - 5
EP - 15
AB - We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.
LA - eng
KW - functional equations; exponential polynomials on Abelian groups; Montel type theorem
UR - http://eudml.org/doc/286778
ER -