Laplace operators on fractals and related functional equations

Gregory Derfel, Peter J. Grabner, Fritz Vogl

Research output: Contribution to journalReview articlepeer-review

24 Scopus citations

Abstract

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-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 compute the Casimir energy of fractals. We give numerical values for this energy for the Sierpiski gasket.

Original languageEnglish
Article number463001
JournalJournal of Physics A: Mathematical and Theoretical
Volume45
Issue number46
DOIs
StatePublished - 23 Nov 2012

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