Positivity and monotony properties of the de Branges functions

By the relation τ˙kn(t)≤0, the de Branges functions τkn(t) are monotonic, and τkn(t)≥0 follows. In this article, we reconsider the de Branges and Weinstein functions, find more relations connecting them with each other, and make the above positivity and monotony result more precise, e.g., by showing τkn(t)≥(n−k+1)e−kt.