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Bernstein type inequality in monotone rational approximation
Bernstein type inequality monotone rational approximation
2010/12/10
The following analog of Bernstein inequality for monotone rational functions is established: if R is an increasing on [−1, 1] rational function of degree n, then R′(x) < 9n 1 − x2 kRk, x ∈...
Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
Ramsey type theorems Dvoretsky’s theorem John’s ellipsoid.
2010/11/29
In this paper we prove the Gromov–Milman conjecture (the Dvoretzky typ theorem) for homogeneous polynomials on Rn, and improve bounds on the number n(d, k)in the analogous conjecture for odd degrees d...