Semiclassical Estimates for Weyl Quantisation

Twisted Covariance and Weyl Quantisation

In this letter we wish to clarify in which sense the tensor nature of the commutation relations [xμ,xν ] = iθμν underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio: “why θ?”

Twisted Covariance vs Weyl Quantisation

In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x,x ] = iθ underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio: “why θ?”

Simplified Semiclassical Propagation Estimates

Semiclassical L Estimates

The purpose of this paper is to use semiclassical analysis to unify and generalize L estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity and order, and apply to operators which are selfadjoint only at the principal level. They are estimates on weakly approximate solutions to semiclassical pseudodifferential equations. To mo...

Universal bounds and semiclassical estimates for eigenvalues

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space. These inequalities lead to universal bounds on spectral gaps and on moments of eigenvalues {λk} that are analogous to those known for Schrödinger operators and the Dirichlet Laplacian, on which the operators of interest are modeled. In addition we produce inequalities that are new even in the model case. These...