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회의 ID: 894 159 2643
Abstract: We learn from the recent paper due to Germain and Myerson on the L2-Lp estimates for spectral projectors on the torus. In contrast with the sphere case, the estimates improve as the length of spectral projectors decreases from 1. However, Bourgain’s conjecture and the corresponding results on the eigenfunction bounds show that the improvement is not true anymore if the length is very small. We investigate the necessary condition and conjecture for this interesting phenomenon and prove a partial result.