20 citations · 21 across the 4 of their papers we have counts for
4 papers
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…
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…