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

20161125 16:30 
20161125 17:30
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Hiroya Ito (The University of ElectroCommunications)

 Spherical harmonics on S^{n1}, which are used extensively in various fields, are harmonic homogeneous polynomials in R^n restricted to the unit sphere S^{n1}. After reviewing some important facts about spherical harmonics, we define spherical functions (vector fields) for the Lame system by restricting to S^{n1} 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^2space on S^{n1}, which is a fundamental property of the spherical harmonics. We also consider the same problem for the Stokes system.