A theorem for symmetric n-linear forms

Abstract

This paper contains an existence theorem describing the way in which the global maximum magnitude of a symmetric n-linear form can be attained on a product of unit spheres. The application of a corollary to the theorem arises in the context of structural mechanics, and a previous attempt at a proof of this has been shown to be invalid. Some interesting aspects of the problem are highlighted by the proof of the theorem, which leads to some results for homogeneous polynomials.