A Spectral Multiplier Theorem associated with a Schr\"odinger Operator

Younghun Hong

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arXiv · 1210.6326

A Spectral Multiplier Theorem associated with a Schr\"odinger Operator

Younghun Hong

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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.

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Younghun Hong. 2012-10-23. A Spectral Multiplier Theorem associated with a Schr\"odinger Operator. https://arxiv.org/abs/1210.6326

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