On the Lebesgue Constants

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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 \( {\mathbbm{S}}^d \), in complex Pd(ℂ) and quaternionic Pd(ℍ) projective spaces, and in the Cayley elliptic plane P16(Cay). In particular, these results supplement the sharp asymptotics established by Fejer (1910) in the case of \( {\mathbbm{S}}^1 \) and by Gronwall (1914) in the case of \( {\mathbbm{S}}^2 \).

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Correspondence to A. K. Kushpel.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 8, pp. 1073–1081, August, 2019.

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Kushpel, A.K. On the Lebesgue Constants. Ukr Math J 71, 1224–1233 (2020) doi:10.1007/s11253-019-01709-5

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