Thursday, November 29, 2012

1211.6536 (Frank Bauer et al.)

On the $l^p$ spectrum of Laplacians on graphs    [PDF]

Frank Bauer, Bobo Hua, Matthias Keller
We study the $p$-independence of spectra of Laplace operators on graphs arising from regular Dirichlet forms on discrete spaces. Here, a sufficient criterion is given solely by a uniform subexponential growth condition. Moreover, under a mild assumption on the measure we show a one-sided spectral inclusion without any further assumptions. We study applications to normalized Laplacians including symmetries of the spectrum and a characterization for positivity of the Cheeger constant. Furthermore, we consider Laplacians on planar tessellations for which we relate the spectral $p$-independence to assumptions on the curvature.
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