2017/05/10 by Geno Nikolov, Nikolov, Geno, Alexei Shadrin +1
Mathematics · #41A17 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1705.03824
openalex publication_date 2017/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let wα(t) := tα e-t, where α> -1, be the Laguerre weight function, and let ‖⋅‖wα be the associated L2-norm, ‖f‖wα = \∫0∞ |f(x)|2 wα(x) dx\1/2 . By Pn we denote the set of algebraic polynomials of degree ≤ n. We study the best constant cn(α) in the Markov inequality in this norm ‖pn'‖wα ≤ cn(α) ‖pn‖wα , pn ∈ Pn , namely the constant cn(α) := suppn ∈ Pn \frac‖pn'‖wα‖pn‖wα . We derive explicit lower and upper bounds for the Markov constant cn(α), as well as for the asymptotic Markov constant c(α)=limn→∞(cn(α))/(n) .