Spectral identities and smoothing estimates for evolution operators
报告人：Sugimoto Mitsuru (Nagoya University, JAPAN)
地点：Room 1365, Sciences Building No.1
Abstract: Smoothing and decay spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the existence (and weak continuity) of the spectral density in a functional setting. Spectral identities for the time evolution of such operators are derived, enabling results concerning comparison principles which yield smoothing estimates for classes of functions of the operators. An important particular case is the derivation of global spacetime estimates for a perturbed operator on the basis of its comparison with the unperturbed operator. A number of applications are given, including smoothing estimates for fractional Laplacians, Stark Hamiltonians and Schr\"odinger operators with potentials. This is joint work with Matania Ben-Artzi (Hebrew University) and Michal Ruzhansky (Imperial college London).