The Lebesgue constants on projective spaces

Abstract

We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgue constants or norms of the Fourier-Laplace projections on the real projective spaces Pd (ℝ). In particular, these results extend sharp asymptotic found by Fejer [2] in the case of (Formula presented) in 1910 and by Gronwall [4] in 1914 in the case of (Formula presented). The case of spheres, (Formula presented), complex and quaternionic projective spaces, Pd(ℂ), Pd(ℍ) and the Cayley elliptic plane P16(Cay) was considered by Kushpel [8].