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, ALEXANDER
(2021)
"The Lebesgue constants on projective spaces,"
Turkish Journal of Mathematics: Vol. 45:
No.
2, Article 14.
https://doi.org/10.3906/mat-1910-111
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss2/14
