Determinant criteria of solvability

V. S. Kalnitsky. "Determinant criteria of solvability." Banach Center Publications 99.1 (2013): 77-86. <http://eudml.org/doc/286159>.

@article{V2013,
abstract = {In the paper [3] the determinant criterion of solvability for the Kuczma equation [4] was given. This criterion appeared in the natural way as barycenter of some mass system. It turned out that determinants do appear in many different situations as solvability criteria. The present article is aimed to review the mostly classical results in the theory of functional equations from this point of view. We begin with classical results of the linear functional equations and the determinant equations solved by F. Neuman. Using natural hierarchy we select some class of well-known equations in order to catch a pattern in the solvability criteria. This approach gives some sort of hypothesis.},
author = {V. S. Kalnitsky},
journal = {Banach Center Publications},
keywords = {functional equation in several variables; determinant criterion; determinant equation},
language = {eng},
number = {1},
pages = {77-86},
title = {Determinant criteria of solvability},
url = {http://eudml.org/doc/286159},
volume = {99},
year = {2013},
}

TY - JOUR
AU - V. S. Kalnitsky
TI - Determinant criteria of solvability
JO - Banach Center Publications
PY - 2013
VL - 99
IS - 1
SP - 77
EP - 86
AB - In the paper [3] the determinant criterion of solvability for the Kuczma equation [4] was given. This criterion appeared in the natural way as barycenter of some mass system. It turned out that determinants do appear in many different situations as solvability criteria. The present article is aimed to review the mostly classical results in the theory of functional equations from this point of view. We begin with classical results of the linear functional equations and the determinant equations solved by F. Neuman. Using natural hierarchy we select some class of well-known equations in order to catch a pattern in the solvability criteria. This approach gives some sort of hypothesis.
LA - eng
KW - functional equation in several variables; determinant criterion; determinant equation
UR - http://eudml.org/doc/286159
ER -