A Spectral Multiplier Theorem associated with a Schr\"odinger Operator
Analysis of PDEs
2015-08-31 v4
Abstract
We establish a spectral multiplier theorem associated with a Schr\"odinger operator H=-\Delta+V(x) in \mathbb{R}^3. We present a new approach employing the Born series expansion for the resolvent. This approach provides an explicit integral representation for the difference between a spectral multiplier and a Fourier multiplier, and it allows us to treat a large class of Schr\"odinger operators without Gaussian heat kernel estimates. As an application to nonlinear PDEs, we show the local-in-time well-posedness of a 3d quintic nonlinear Schr\"odinger equation with a potential.
Cite
@article{arxiv.1210.6326,
title = {A Spectral Multiplier Theorem associated with a Schr\"odinger Operator},
author = {Younghun Hong},
journal= {arXiv preprint arXiv:1210.6326},
year = {2015}
}