Gram matrices of reproducing kernel Hilbert spaces over graphs IV. (Quadratic inequalities for graph Laplacians)

We study the relationship between a graph and its subgraph from a viewpoint of functional analysis. As an application of the theory of quasi-orthogonal integrals developed by de Branges–Rovnyak and Vasyunin–Nikol'skiĭ, quadratic inequalities for graph Laplacians are given.