Graph‐like spaces approximated by discrete graphs and applications

We define a distance between energy forms on graph-like metric measure space and suitable discrete weighted graph using the concept of quasi-unitary equivalence. apply this result to graphs, manifolds (e.g. small neighbourhood an embedded graph) or pcf self-similar fractals as spaces with associated canonical Laplacians, e.g., Kirchhoff Laplacian resp. (Neumann) manifold (with boundary), express in terms geometric quantities. In particular, we show that there is sequence domains converging fractal such corresponding converge form. As consequence, spectra functions Laplacians converge, latter operator norm.