Abstract theory of pointwise decay with applications to wave and Schrödinger equations
We prove pointwise in time decay estimates via an abstract conjugate operator method. This is then applied to a large class of dispersive equations.
math.AP↗
arXiv subjects
Manuel Larenas
Publications and source records attributed to Manuel Larenas.
Abstract theory of decay estimates: perturbed Hamiltonians
For two self-adjoint operators $H,A$ we show that a general commutation relation of type $[H,\mathrm{i}A]=Q(H)+K$, in addition to regularity of $H$ and Kato-smoothness of $K$, guarantee pointwise in time decay rates of diverse order. The methodology is based on the construction of a modified conjugate operator $\tilde{A}$ that reduces the problem to previously developed estimates when $K=0$. Our results apply to energy thresholds and do not rely on resolvent estimates. We discuss applications for the Schrödinger equation (SE) with potential of critical decay, and for the free SE on an asymptotically flat manifold.
math.AP↗