Energy and Laplacian on Hanoi-type Fractal Quantum Graphs
نویسنده
چکیده
We study energy and spectral analysis on compact metric spaces which we refer to as fractal quantum graphs. These are spaces that can be represented as a (possibly infinite) union of 1-dimensional intervals and a totally disconnected (possibly uncountable) compact set, which roughly speaking represents the set of junction points. These spaces include classical quantum graphs and fractal spaces such as the Hanoi attractor, which is weakly self-similar. We begin with proving the existence of a resistance form on the Hanoi attractor, and discuss the spectral asymptotics of the Laplacians corresponding to weakly self-similar measures. We then state and prove the existence of resistance forms on general fractal quantum graphs. Finally, we prove spectral asymptotics for a large class of weakly self-similar fractal quantum graphs.
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تاریخ انتشار 2014