Spectral analysis on infinite Sierpiński fractafolds

Spectral Analysis on Infinite Sierpinski Fractafolds

Abstract. A fractafold, a space that is locally modeled on a specified fractal, is the fractal equivalent of a manifold. For compact fractafolds based on the Sierpiński gasket, it was shown by the first author how to compute the discrete spectrum of the Laplacian in terms of the spectrum of a finite graph Laplacian. A similar problem was solved by the second author for the case of infinite blow...

Groupoid Actions on Fractafolds

We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault–Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault– Deaconu groupoid itself. We also show that when the bundle is locally compact the associated C∗-algebra is primitive and has a densely defin...

Spectral Elements on Infinite Domains

an infinite planar array of rectangular microstrip patch antenna analysis

the methods which are used to analyze microstrip antennas, are divited into three categories: empirical methods, semi-empirical methods and full-wave analysis. empirical and semi-empirical methods are generally based on some fundamental simplifying assumptions about quality of surface current distribution and substrate thickness. thses simplificatioms cause low accuracy in field evaluation. ful...

Harmonic Coordinates on Finitely Connected Fractafolds

We define finitely connected fractafolds, which are generalizations of p.c.f. self-similar sets introduced by Kigami and of fractafolds introduced by Strichartz. Any self-similarity is not assumed, and countably infinite ramification is allowed. We prove that if a fractafold has a resistance form in the sense of Kigami that satisfies certain assumptions, then there exists a weak Riemannian metr...