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In this paper, we study the mapping property form $L^p$ to $L^q$ of theresolvent of the Fourier multiplier operators and scattering theory ofgeneralized Schr\"odinger operators. Though the first half of the subject isstudied in [4], we extend their result to away from the duality line and wealso study the H\"older continuity of the resolvent.

Limiting absorption principle on $L^p$-spaces and scattering theory