Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

Details Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

2010-11-24

arxiv.org/abs/1011.5485v4

Mathematics

Functional Analysis

Scientific paper

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature.

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