Sampling theory for functions with fractal spectrum.
Cauchy transforms of self-similar measures.
Sampling on the Sierpinski gasket.
Densities of self-similar measures on the line.
Outer boundaries of self-similar tiles.
Numerical experiments in Fourier asymptotics of Cantor measures and wavelets.
Constructing a Laplacian on the diamond fractal.
Gibbs' Phenomenon and Arclength.
Piecewise Linear Wavelets on Sierpinski Gasket Type Fractals.
Self-Similaritiy in Harmonic Analysis.
Sobolev spaces
Fubini-type theorems
Invariant pseudo-differential operators on a Lie group
Homeomorphisms of fractafolds
We classify all homeomorphisms of the double cover of the Sierpiński gasket in n dimensions. We show that there is a unique homeomorphism mapping any cell to any other cell with prescribed mapping of boundary points, and any homeomorphism is either a permutation of a finite number of topological cells or a mapping of infinite order with one or two fixed points. In contrast we show that any compact fractafold based on the level-3 Sierpiński gasket is topologically rigid.
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