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The purpose of this article is to prove that – under reasonable assumptions – the canonical energy form on a graph-like manifold is quasi-unitarily equivalent with the energy form on the underlying discrete graph. Then we will apply this to approximate the standard energy form on the Sierpiński gasket by a family of energy forms on suitable graph-like manifolds. Mathematics subject classification (2010): 28A80, 05C75, 47A58.

Convergence of Laplacians on smooth spaces towards the fractal Sierpiński gasket