Published November 23, 2012
| Version v1
Journal article
Laplace operators on fractals and related functional equations
- 1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva 84105 (Israel)
- 2. Institut für Analysis und Computational Number Theory, Technische Universität Graz, Steyrergasse 30, A-8010 Graz (Austria)
- 3. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstraße 8–10, A-1040 Wien (Austria)
Description
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 Sierpiński gasket. (topical review)
Availability note (English)
Available from http://dx.doi.org/10.1088/1751-8113/45/46/463001Additional details
Identifiers
Publishing Information
- Journal Title
- Journal of Physics. A, Mathematical and Theoretical (Online)
- Journal Volume
- 45
- Journal Issue
- 46
- Journal Page Range
- [34 p.]
- ISSN
- 1751-8121
INIS
- Country of Publication
- United Kingdom
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 44046654
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- COMPARATIVE EVALUATIONS; EUCLIDEAN SPACE; FRACTALS; LAPLACIAN; POINCARE GROUPS; SCHWINGER FUNCTIONAL EQUATIONS; SPECTRA
- Descriptors DEC
- DIFFERENTIAL EQUATIONS; EQUATIONS; EVALUATION; LIE GROUPS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; RIEMANN SPACE; SPACE; SYMMETRY GROUPS