Szego limit theorems on the Sierpinski gasket

TL;DR

This paper extends Szego limit theorems to the fractal setting of the Sierpinski gasket by leveraging localized eigenfunctions of the Laplacian, providing new insights into spectral properties on fractals.

Contribution

It formulates and proves Szego limit theorems on the Sierpinski gasket, a novel application in fractal analysis, and relates results to equally distributed sequences.

Findings

Established analogues of Szego limit theorems on the Sierpinski gasket.

Utilized localized eigenfunctions of the Laplacian for proofs.

Connected spectral results to equally distributed sequences.

Abstract

We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket to formulate and prove analogues of the strong Szego limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of equally distributed sequences.