Turkish Journal of Mathematics
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 $\mathrm{P}^{d}(\mathbb{R})$. In particular, these results extend sharp asymptotic found by Fejer [2] in the case of $\mathbb{S}^{1}$ in 1910 and by Gronwall [4] in 1914 in the case of $\mathbb{S}^{2}$. The case of spheres, $\mathbb{S}^{d}$, complex and quaternionic projective spaces, $\mathrm{P}^{d}(\mathbb{C})$, $% \mathrm{P}^{d}(\mathbb{H})$ and the Cayley elliptic plane $\mathrm{P}^{16}(% \mathrm{Cay})$ was considered by Kushpel [8].
DOI
10.3906/mat-1910-111
Keywords
Lebesgue constant, Fourier-Laplace projection, Jacoby polynomia
First Page
856
Last Page
863
Recommended Citation
KUSHPEL, A (2021). The Lebesgue constants on projective spaces. Turkish Journal of Mathematics 45 (2): 856-863. https://doi.org/10.3906/mat-1910-111
