Výsledky vyhledávání - "Heilman, Steven M."

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Orthogonal Polynomials with Respect to Self-Similar Measures

Autor: Heilman, Steven M., Owrutsky, Philip, Strichartz, Robert S.

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 properties of the polynomials, both on the Cantor set and in the gaps of the

Externí odkaz: http://arxiv.org/abs/0910.0631

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Localized Eigenfunctions: Here You See Them, There You Don't

Autor: Heilman, Steven M., Strichartz, Robert S.

This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.
Comment: 5 pages, 12 figures, 2 tables, to appear, Not

Externí odkaz: http://arxiv.org/abs/0909.0783

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Homotopies of Eigenfunctions and the Spectrum of the Laplacian on the Sierpinski Carpet

Autor: Heilman, Steven M., Strichartz, Robert S.

Consider a family of bounded domains $\Omega_{t}$ in the plane (or more generally any Euclidean space) that depend analytically on the parameter $t$, and consider the ordinary Neumann Laplacian $\Delta_{t}$ on each of them. Then we can organize all t

Externí odkaz: http://arxiv.org/abs/0908.2942

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Outer Approximation of the Spectrum of a Fractal Laplacian

Autor: Berry, Tyrus, Heilman, Steven M., Strichartz, Robert S.

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 sequence of domains that approximate K from the outside. The method a

Externí odkaz: http://arxiv.org/abs/0904.3757

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