On \(E\)-Pólya frequency functions (Q933460)

Let \(E\) be a subset of \(\mathbb R\). A real function \(f\) defined on \(\mathbb R\) is an \(E\)-Pólya frequency function if the kernel \(f(u-x)\) is totally positive on the set \(E \times\mathbb R\) and \(f\) is integrable on \(\mathbb R\). In the paper the author studies what conditions imposed on \(E\) imply that an \(E\)-Pólya frequency function is a Pólya frequency function.