Michael I Ganzburg, Miquel Saucedo, Sergey Tikhonov
Published 2024-03-19Version 1
In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $\|f^{(s)}\|_q \lesssim C(s, p, q)\left\|f\right\|_p,\,0<p<q \leq\infty$, for trigonometric polynomials and entire functions of exponential type. We obtain the optimal behavior of the constant with respect to the smoothness parameter $s$.
$L$-approximation of $B$-splines by trigonometric polynomials
Extension of Vietoris' inequalities for positivity of trigonometric polynomials
On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness
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