46 citations · 191 across the 47 of their papers we have counts for
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Analysis of the Laplacian and Spectral Operators on the Vicsek Set
Sarah Constantin, Robert S. Strichartz, Miles Wheeler
We study the spectral decomposition of the Laplacian on a family of fractals that includes the Vicsek set for , extending earlier research on the Sierpinski G…
Localized Eigenfunctions: Here You See Them, There You Don't
Steven M. Heilman, Robert S. Strichartz
This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eige…
Homotopies of Eigenfunctions and the Spectrum of the Laplacian on the Sierpinski Carpet
Steven M. Heilman, Robert S. Strichartz
Consider a family of bounded domains in the plane (or more generally any Euclidean space) that depend analytically on the parameter , and consider the ordinary Neumann L…
Outer Approximation of the Spectrum of a Fractal Laplacian
Tyrus Berry, Steven M. Heilman, Robert S. Strichartz
We present a new method to approximate the Neumann spectrum of a Laplacian on a fractal K in the plane as a renormalized limit of the Neumann spectra of the standard Laplacian on a…