4 papers · 1 filter
A Gutzwiller trace formula for singular potentials
Jared Wunsch, Mengxuan Yang, Yuzhou Joey Zou
The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectori…
Logarithmic wave decay for short range wavespeed perturbations with radial regularity
Gayana Jayasinghe, Katrina Morgan, Jacob Shapiro +1
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbatio…
Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
Fabrice Baudoin, Li Chen, Meng Yang
We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform vo…
A direct proof of the cutoff Sobolev inequality on the Sierpiński gasket
Meng Yang
We present a direct proof of the cutoff Sobolev inequality on the Sierpiński gasket, which has long been regarded as highly non-trivial in the context of heat kernel estimates.