Szegö Limit Theorems on the Sierpiński Gasket

Szegö Limit Theorems on the Sierpiński Gasket

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.

Hanoi attractors and the Sierpiński gasket

The famous game Towers of Hanoi is related with a family of so–called Hanoi–graphs. We regard these non self–similar graphs as geometrical objects and obtain a sequence of fractals (HGα)α converging to the Sierpiński gasket which is one of the best studied fractals. It is shown that this convergence holds not only with respect to the Hausdorff distance, but that also Hausdorff dimension does co...

Szegö limit theorems for operators with almost periodic diagonals Steffen

The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections PnT (a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.

Sierpiński gasket graphs and some of their properties

Block-Space GPU Mapping for Embedded Sierpiński Gasket Fractals

This work studies the problem of GPU thread mapping for a Sierpiński gasket fractal embedded in a discrete Euclidean space of n × n. A block-space map λ : Z2E 7→ Z 2 F is proposed, from Euclidean parallel space E to embedded fractal space F, that maps in O(log 2 log 2 (n)) time and uses no more than O(n) threads with H ≈ 1.58... being the Hausdorff dimension, making it parallel space efficient....