Abstract:We study an asymptotic formula for the number of negative eigenvalues of Schrödinger operators on unbounded fractal spaces, which admit a cellular decomposition. We first give some sufficient conditions for Weyl-type asymptotic formula to hold. Second, we verify these conditions for the infinite blowup of Sierpiński gasket and unbounded generalized Sierpiński carpets. Finally, we demonstrate how the result can be applied to the infinite blowup of certain fractals associated with iterated function systems with … Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.