Sanghyuk Lee

Title: Estimates for the resolvent of the Laplacian

Abstract: This talk mainly concerns with boundedness of the resolvent of the Laplacian, which has application to various related problems such as, uniform Sobolev inequality, unique continuation, and spectral analysis. We discuss the sharp bound in terms of the spectral parameter and the optimal range on which the estimate holds. We also consider sharp range of boundedness of related multiplier operators. This talk is based on joint work with Yehyun Kwon and Eunhee Jeong.