A Spectral Multiplier Theorem Associated with a Schrodinger Operator

초록

We establish a Hormander type spectral multiplier theorem for a Schrodinger operator in , provided V is contained in a large class of short range potentials. This result does not require the Gaussian heat kernel estimate for the semigroup , and indeed the operator H may have negative eigenvalues. As an application, we show local well-posedness of a 3d quintic nonlinear Schrodinger equation with a potential.

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