18. Harmonic polynomials and spherical harmonics

Corrections

Not that it matters very much, but the coefficients c_ijk in the cubic part of the polynomial at 1:30 were meant to be called d_ijk (to be consistent with the naming of the lower-order coefficients a, b_i and c_ij). Also, at 35:12, it would have been more consistent to denote the harmonic polynomials p_m, p_m-2, … by h_m, h_m-2, … instead.

At 47:15, it's of course the square of the L² norm (rather than the L² norm itself) that equals ⟨f,f⟩.

At 49:05, the third bullet item is wrong. The correct statement is that the set of restrictions p|_S, as p ranges over all polynomials, is dense in L²(S).

Sidansvarig: Hans Lundmark
Senast uppdaterad: 2025-04-30