Gregory Derfel, Peter Grabner, Fritz Vogl
We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket.
View original:
http://arxiv.org/abs/1206.1211
No comments:
Post a Comment