## 偏微分方程式セミナー(2016/11/25): Spherical harmonics and their analogues for Lame’s and Stokes’ systems, 伊東 裕也 氏 (電気通信大学)

2016年 　 11月 25日 16時 30分 ～ 2016年 　 11月 25日 17時 30分

Spherical harmonics on S^{n-1}, which are used extensively in various fields, are harmonic homogeneous polynomials in R^n restricted to the unit sphere S^{n-1}. After reviewing some important facts about spherical harmonics, we define spherical functions (vector fields) for the Lame system by restricting to S^{n-1} homogeneous polynomial solutions of the equation μ∆u + (λ+μ)∇(div u) = 0 in R^n. We show that those spherical functions span a dense subspace of the L^2-space on S^{n-1}, which is a fundamental property of the spherical harmonics. We also consider the same problem for the Stokes system.