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.
Extremal Signatures
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abstract
Let $E= A - iB$ be a Hermite-Biehler entire function of exponential type $\tau/2$ where $A$ and $B$ are real entire, and consider $d\mu(x) = dx/|E(x)|^2$. We show that the sign of the product $A B$ is an extremal signature for the space of functions of exponential type $\tau$ with respect to the norm of $L^1(\mu)$. This allows us to find best approximations by entire functions of exponential type $\tau$ in $L^1(\mu)$-norm to certain special functions (e.g., the Gaussian and the Poisson kernel).
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math.CA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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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.