PDE Seminar (2016/11/25): Spherical harmonics and their analogues for Lame’s and Stokes’ systems, Hiroya Ito (The University of Electro-Communications)

2016-11-25 16:30 - 2016-11-25 17:30
Faculty of Science Building #3, Room 309
Hiroya Ito (The University of Electro-Communications)
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.