We develop a unified approach to proving Lp−Lq boundedness of spectral projectors, the resolvent Laplace-Beltrami operator and its derivative on Hd. In case when p q are in duality, dependence implicit constant is shown be sharp. also give partial results question Fourier extension operator. As an application, we prove smoothing estimates for free Schrödinger equation Hd limiting absorption pri...

Spectral methods have been widely used to study the structural properties of unlabeled datasets. In this work we describe a clustering approach that exploits the structural properties in the configuration space of objects as well as the spectral sub-space, quite unlike earlier methods. We propose a spectral clustering approach, where we formalize the notion of clusters as vertices of a simplex ...