On the Lebesgue constants - Kushpel, A. K. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
UDC 517.5 We give the solution of a classical problem of approximation theory on sharp asymptotic of the Lebesgue constants ornorms of the Fourier – Laplace projections on the real spheres $\mathbb{S}^{d},$ complex $P^{d}(\mathbb{C})$ and quaternionic $P^{d}(\mathbb{H})$ projective spaces, and the Cayley elliptic plane $P^{16}(Cay).$ In particular, these results extend sharp asymptotic found by Fejer in thecase of $\mathbb{S}^{1}$ in 1910 and by Gronwall in 1914 in the case of $\mathbb{S}^{2}$ .