Gradients of Laplacian Eigenfunctions on the Sierpinski Gasket
Jessica L. DeGrado, Luke G. Rogers, Robert S. Strichartz
TL;DR
This paper derives explicit formulas for the harmonic gradients of Laplacian eigenfunctions on the Sierpinski Gasket using spectral decimation, expressed through special functions involving infinite products.
Contribution
It introduces a novel spectral decimation approach to compute gradients of eigenfunctions on fractals, with explicit formulas involving infinite product functions.
Findings
Explicit formulas for harmonic gradients on the Sierpinski Gasket
Use of spectral decimation for fractal eigenfunction analysis
Representation of formulas via infinite product special functions
Abstract
We use spectral decimation to provide formulae for computing the harmonic gradients of Laplacian eigenfunctions on the Sierpinski Gasket. These formulae are given in terms of special functions that are defined as infinite products.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical Analysis and Transform Methods · Topological and Geometric Data Analysis