The paper proves that the asymptotic Nikolskii constant L^*(d) decays exponentially with dimension d (0.5^d lower bound, ~0.857^d upper bound with slow factor), by identifying the linked Bessel extremal constant I_alpha with a hypergeometric function for alpha >= -0.272.
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Estimates of the asymptotic Nikolskii constants for spherical polynomials
The paper proves that the asymptotic Nikolskii constant L^*(d) decays exponentially with dimension d (0.5^d lower bound, ~0.857^d upper bound with slow factor), by identifying the linked Bessel extremal constant I_alpha with a hypergeometric function for alpha >= -0.272.