Question about an obscure notation

66 Views Asked by At

I have run across the following mathematical notation in an old paper and I am not sure what it means; I have also asked colleagues and they don't know what it means either. The notation is:

$$ \underset{\scriptstyle 0 \leq \theta \leq 2\pi}{\Large \varDelta} \arg \det \psi(e^{i\theta}) = 0 . $$

To be specific, I'm not sure what the big $\varDelta$ means here.

For context, this equation establishes a condition that must hold before using a result on the determinant of block Toeplitz matrices. Here $\psi(z)$ is a matrix, where

$$ \psi(z) = \sum_{j=-\infty}^\infty \psi_j z^j $$

and $\psi_j$ is a sequence of matrices, a subsequence of which form the blocks of the block Toeplitz matrix.

The condition appears in equation (1.2) of the following paper: H. Widom, "Asymptotic behaviour of block Toeplitz matrices and determinants," Adv. Math 13, 284-322, 1974. The citations of the paper didn't give much help.

Thanks in advance for any insight.