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学术活动
“数通古今，学贯中外”学术讲座第七十期预告【韩晓龙】
编辑： 数学学院 董学敏 时间：2014-06-12
各位老师：
6月16日(周一) 下午 2:00-3:00, 研究生楼104有来自澳大利亚的韩晓龙老师做报告，敬请留意！
报告人: 韩晓龙, 澳大利亚国立大学
Title: Spherical harmonics with maximal norm growth
Abstract: Sogge’s Lp estimates bound the Lp norms of normalized eigenfunctions on smooth and compact manifolds. They are also sharp on the sphere, with maximizers as Gaussian beams for small p and zonal harmonics for large p. In this talk, we investigate the density of these maximizers in the orthonormal eigenfunction basis, and construct a positive density subsequence of orthonormal spherical harmonics which achieves the maximal Lp norm growth for all small p. This gives an example of a Riemannian surface supporting such subsequence of eigenfunctions. Furthermore, we provide an explicit lower bound on the density in this example.
祝好!