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Fix $i$. If $t<t_i$, all knot values of the function $x\mapsto (x-t{)}_{+}^{k-1}$ agree with a polynomial of degree $k-1$. Its order-$k$ divided difference vanishes. If $t>t_{i+k}$, all the knot values are zero, so the same divided difference again vanishes. Thus the support is finite:The support and Gram bandwidth of B-splines also holds at repeated knots: the same conclusion follows with the standard limiting convention. If $j\ge i+k$, then $t_j\ge t_{i+k}$, so the two supports have no positive-length overlap. An endpoint intersection contributes zero to the integral defining $G_{ij}$. The case $i\ge j+k$ is identical. HenceFor strictly increasing knots, B-splines whose indices differ by $k-1$ overlap on a positive-length interval and their product is positive there, so this universal bound is sharp. In standard matrix terminology the half-bandwidth is $k-1$ and the full bandwidth is $2k-1$; the paper's integer $d$ is $k$.