# Szegö Limit Theorems on the Sierpiński Gasket

@article{Okoudjou2008SzegLT, title={Szeg{\"o} Limit Theorems on the Sierpiński Gasket}, author={Kasso A. Okoudjou and Luke G. Rogers and Robert S. Strichartz}, journal={Journal of Fourier Analysis and Applications}, year={2008}, volume={16}, pages={434-447} }

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

## 9 Citations

### Some spectral properties of pseudo-differential operators on the Sierpinski Gasket

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### Spectral Analysis Beyond $$\ell ^2$$ on Sierpinski Lattices

- Mathematics
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We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of $\mathbb{C}$, remains the same for any $\ell^p$ spaces. Second, we…

### Gaps in the spectrum of the Laplacian on $3N$-Gaskets

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This article develops analysis on fractal $3N$-gaskets, a class of post-critically finite fractals which include the Sierpinski triangle for $N=1$, specifically properties of the Laplacian $\Delta$…

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. We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of C , remains the same for any (cid:96) p spaces. Second, we…

### Spectral dimension and Bohr's formula for Schrödinger operators on unbounded fractal spaces

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We establish an asymptotic formula for the eigenvalue counting function of the Schrödinger operator − Δ + V ?> for some unbounded potentials V on several types of unbounded fractal spaces. We give…

### Spectral analysis on infinite Sierpiński fractafolds

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- 2010

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- MathematicsFractals
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We study the graphs associated with Vicsek sets in higher dimensional settings. First, we study the eigenvalues of the Laplacians on the approximating graphs of the Vicsek sets, finding a general…

### Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets

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- 2010

AbstractIn this paper we study the boundary limit properties of harmonic functions on ℝ+×K, the solutions u(t,x) to the Poisson equation
$$\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,$$ where K…

### Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

- MathematicsCalculus of Variations and Partial Differential Equations
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We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a weak Bakry–Émery…

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