Some spectral properties of pseudo-differential operators on the Sierpinski Gasket
Marius Ionescu, Kasso A. Okoudjou, and Luke G. Rogers
TL;DR
This paper establishes strong Sz"ego limit theorems for pseudodifferential operators on the Sierpinski gasket, leveraging localized eigenfunctions of the Laplacian to analyze spectral properties on this fractal.
Contribution
It introduces new spectral analysis results for pseudodifferential operators on fractals, specifically the Sierpinski gasket, using localized eigenfunctions.
Findings
Proves strong Sz"ego limit theorems for certain pseudodifferential operators on the gasket.
Utilizes the existence of localized eigenfunctions of the Laplacian.
Provides foundational spectral properties for analysis on fractals.
Abstract
We prove versions of the strong Sz\"ego limit theorem for certain classes of pseudodifferential operators defined on the Sierpi\'nski gasket. Our results used in a fundamental way the existence of localized eigenfunctions for the Laplacian on this fractal.
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