We compute asymptotic formulas for the k th Fourier coefficients of b λ n, where b λ (z)= z-λ 1-
λ z is the Blaschke factor associated to λ∈ D, k∈[0,∞) and n is a large integer. We …

We derive new estimates on analytic capacities of finite sequences in the unit disc in Besov
spaces with zero smoothness, which sharpen the estimates obtained by NK Nikolski in 2005 …

We investigate the large n behavior of Jacobi polynomials with varying parameters P n (a n+
α, b n+ β)(1− 2 λ 2) for a, b>− 1 and λ∈(0, 1). This is a well-studied topic in the literature but …

Given a finite Blaschke product we prove asymptotically sharp estimates on the-norm of the
sequence of the Fourier coefficients of as tends to. This norm decays as for some …

In 2005, N. Nikolski proved among other things that for any $ r\in (0, 1) $ and any $ K\geq 1$,
the condition number $ CN (T)=\Vert T\Vert\cdot\Vert T^{-1}\Vert $ of any invertible n …

The utility of the (weighted) van der Corput inequalities or of the stationary phase method is
illustrated with various examples borrowed from: differentiability issues (Riemann's function …

This note surveys recent strategies to estimate the condition number CN (T)= ‖ T ‖ ⋅ ‖ T^-
1 ‖ CN (T)=‖ T‖·‖ T-1‖ of complex n * nn× n matrices T with given spectrum. More …