50 citations · 236 across the 25 of their papers we have counts for
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Bernstein inequalities with nondoubling weights
Andriy Bondarenko, Sergey Tikhonov
We answer Totik's question on weighted Bernstein's inequalities showing that holds for all trigonom…
Bernstein type inequality in monotone rational approximation
Andriy V. Bondarenko, Maryna S. Viazovska
The following analog of Bernstein inequality for monotone rational functions is established: if is an increasing on rational function of degree , then $$ R'(x)<\fra…
Spherical designs via Brouwer fixed point theorem
Andriy V. Bondarenko, Maryna S. Viazovska
For each N>=c_d*n^{2d*(d+1)/(d+2)} we prove the existence of a spherical n-design on S^d consisting of N points, where c_d is a constant depending only on .
New asymptotic estimates for spherical designs
Andriy V. Bondarenko, Maryna S. Viazovska
Let N(n, t) be the minimal number of points in a spherical t-design on the unit sphere S^n in R^{n+1}. For each n >= 3, we prove a new asymptotic upper bound N(n, t) <= C(n)t^{a_n}…