Generalized Eigenfunctions and a Borel Theorem on the Sierpinski Gasket

by Kasso A Okoudjou, Luke G. Rogers and Robert S. Strichartz

We prove there exist exponentially decaying generalized eigenfunctions on a blow-up of the Sierpinski gasket with boundary. These are used to show a Borel-type theorem, specifically that for a prescribed jet at the boundary point there is a smooth function having that jet.

Published version in Canad Math Bull