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- W2015209462 abstract "It is shown that a Bernstein-type inequality always implies its Szegő-variant, and several corollaries are derived. Then, it is proven that the original Bernstein inequality on derivatives of trigonometric polynomials implies both Videnskii’s inequality (which estimates the derivative of trigonometric polynomials on a subinterval of the period), as well as its half-integer variant. The methods for these two results are then combined to derive the general sharp form of Videnskii’s inequality on symmetric E ⊂ [ − π , π ] sets. The sharp Bernstein factor turns out to be 2 π times the equilibrium density of the set Γ E = { e i t | t ∈ E } on the unit circle C 1 that corresponds to E when we identify C 1 by R / ( mod 2 π ) ." @default.
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- W2015209462 date "2012-10-01" @default.
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- W2015209462 title "Bernstein-type inequalities" @default.
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- W2015209462 doi "https://doi.org/10.1016/j.jat.2012.03.002" @default.
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