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math.SP2012★ 53 cited
Laplace Operators on Fractals and Related Functional Equations
Gregory Derfel, Peter Grabner, Fritz Vogl
We give an overview over the application of functional equations, namely the classical Poincaré and renewal equations, to the study of the spectrum of Laplace operators on self-sim…
math.SP2005★ 21 cited
The Zeta Function of the Laplacian on Certain Fractals
Gregory Derfel, Peter Grabner, Fritz Vogl
We prove that the zeta-function of the Laplacian on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We char…