Steven M. Heilman

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20092026

most citedLocalized Eigenfunctions: Here You See Them, There You Don't

20 citations · 42 across the 28 of their papers we have counts for

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math.AP2009★ 20 cited

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…

math.AP2009

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 $Ω_{t}$ in the plane (or more generally any Euclidean space) that depend analytically on the parameter $t$ , and consider the ordinary Neumann L…

math.AP2009★ 1 cited

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…