“數(shù)通古今，學(xué)貫中外”學(xué)術(shù)講座第七十期預(yù)告【韓曉龍】
發(fā)布日期：2014-06-12
各位老師：
6月16日(周一) 下午 2:00-3:00, 研究生樓104有來自澳大利亞的韓曉龍老師做報告，敬請留意！
報告人: 韓曉龍, 澳大利亞國立大學(xué)
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!