Fractal Zeta Functions in Metric Spaces
- Author(s): Henderson, Alexander Mark
- Advisor(s): Lapidus, Michel
- et al.
Fractal zeta functions associated to bounded subsets of Euclidean spaces relate the geometry of a set to the spectrum of a Laplace operator defined on that set, thereby making it possible to rephrase certain spectral problems in terms of the set's geometry, and vice versa. We generalize the global theory of fractal zeta functions in Euclidean spaces to a broader class of metric spaces with finite Assouad dimension. We also introduce a local theory which gives a more refined tool for analyzing multifractal measures.