IJPAM: Volume 60, No. 4 (2010)

REPRESENTATIONS THEOREMS FOR SCALAR FUNCTIONS
IN A 4-DIMENSIONAL EUCLIDEAN SPACE

S. Montisci$^1$, S. Pennisi$^2$
$^{1,2}$Dipartimento di Matematica ed Informatica
Universitá degli Studi di Cagliari
72, Via Ospedale, Cagliari, 09124, ITALY
$^1$e-mail: montiscistefania@tiscali.it
$^2$e-mail: spennisi@unica.it


Abstract.In a 4-dimensional Euclidean space, representations theorems are obtained here for scalar valued isotropic functions depending on an arbitrary number of scalars, skew-symmetric second order tensors and symmetric second order tensors; at least one of these last ones is assumed to have an eigenvalue with multiplicity 1. The case with at least a non null vector, among the independent variables, has already been treated in literature; so it is here not treated. The result is a finite, but long, set of scalar valued isotropic functions such that every other scalar function of the same variables can be expressed as a function of the elements of this set. The methodology used to obtain this set is directed in trying to use similar representation theorems, already known in literature for the 3-dimensional case.

Received: March 30, 2010

AMS Subject Classification: 15A72

Key Words and Phrases: representations theorems, scalar valued isotropic functions, skew-symmetric second order tensors, symmetric second order tensors

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 4