Younghun Hong
Published 2012-10-23, updated 2015-08-28Version 4
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.
On an optimal potential of Schrödinger operator with prescribed $m$ eigenvalue
Gaussian heat kernel estimates: from functions to forms
An $L^p$-spectral multiplier theorem with sharp $p$-specific regularity bound on Métivier groups
![QR code for arXiv:1210.6326 [math.AP]](http://oss.arxitics.com/images/favicon.svg)