On the Lebesgue Constants

Abstract

We present the solution of a classical problem of approximation theory about the sharp asymptotics of Lebesgue constants or the norms of Fourier-Laplace projections on the real sphere S-d, in complex P-d (C) and quaternionic P-d(H) projective spaces, and in the Cayley elliptic plane P-16(Cay). In particular, these results supplement the sharp asymptotics established by Fejer (1910) in the case of S-1 and by Gronwall (1914) in the case of S-2.