46 citations · 191 across the 47 of their papers we have counts for
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Orthogonal Polynomials with Respect to Self-Similar Measures
Steven M. Heilman, Philip Owrutsky, Robert S. Strichartz
We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting proper…
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…
Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals
Luke G Rogers, Robert S. Strichartz, Alexander Teplyaev
We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimat…
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…