An extension of Herglotz's theorem to the quaternions

D. Alpay, F. Colombo, D. P. Kimsey +1

A classical theorem of Herglotz states that a function $n\mapsto r(n)$ from $\mathbb{Z}$ into ${\mathbb{C}}^{s\times s}$ is positive definite if and only there exists a $\mathbb C^{s\t…