A geometric estimate on the norm of product of functionals Original Research Article

The open problem of determining the exact value of the n-th linear polarization constant cn of image has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of supshort parallelyshort parallel=1midleft angle bracketx1, yright-pointing angle bracket cdots, three dots, centered left angle bracketxn, yright-pointing angle bracketmid, where x1, … , xn are unit vectors in image. The new estimate is given in terms of the eigenvalues of the Gram matrix [left angle bracketxi, xjright-pointing angle bracket] and improves upon earlier estimates of this kind. However, the intriguing conjecture cn = nn/2 remains open.