Convolution roots of radial positive definite functions with compact support
Convolution roots of radial positive definite functions with compact support
A classical theorem of Boas, Kac, and Krein states that a characteristic function $\varphi$ with $\varphi (x) = 0$ for $|x| \geq \tau$ admits a representation of the form \[ \varphi (x) = \int \! u(y) \hspace {0.2mm} \overline {u(y+x)} \mathrm {d}y, \qquad x \in \mathbb {R}, \] where the …