Abstract
The Laplace operator on the Sierpiński gasket. The Laplace operator on Euclidean space and its analogue on graphs. Maximum principle for harmonic functions. Eigenfunctions of the Laplace operator on the Sierpiński gasket. Comparing the spectra of the Laplace operator on different approximations.
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Notes
- 1.
That is, functions that transform in a prescribed way under the action of the group. Details are explained in textbooks on representation theory.
- 2.
Another formulation: the eigenvalues and eigenvectors of A are the critical values and critical points of the function \(Q(v) := \frac{Q_{1}(v)} {Q_{0}(v)}\) on \(V \setminus \{0\}.\)
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Kirillov, A.A. (2013). The Laplace Operator on the Sierpiński Gasket. In: A Tale of Two Fractals. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-8382-5_2
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DOI: https://doi.org/10.1007/978-0-8176-8382-5_2
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