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math.NA2010★ 1 cited
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…
math.NA2008★ 14 cited
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 .
math.NA2008
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}…