integral Lipschitz filter

Let $h(\lambda )$ be the spectral representation of a convolutional graph filter. $h(\lambda )$ is integral lipschitz on interval $T\subset \mathbb{R}$ means there exists some $c\in \mathbb{R}$ such that

ie, $h(\lambda )$ is lipschitz with a constant inversely proportional to the interval's midpoint

Letting ${\lambda }^{\prime }\to \lambda$, we get

This means that the filter can't change for large $\lambda$.