2017/01/26 by Geno Nikolov, Nikolov, Geno, Alexei Shadrin +1
Mathematics · #41A17 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1701.07682
openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let wλ(t) := (1-t2)λ-1/2, where λ> -(1)/(2), be the Gegenbauer weight function, let ‖⋅‖wλ be the associated L2-norm, ‖f‖wλ = \∫-11 |f(x)|2 wλ(x) dx\1/2 , and denote by Pn the space of algebraic polynomials of degree ≤ n. We study the best constant cn(λ) in the Markov inequality in this norm ‖pn'‖wλ ≤ cn(λ) ‖pn‖wλ , pn ∈ Pn , namely the constant cn(λ) := suppn ∈ Pn \frac‖pn'‖wλ‖pn‖wλ . We derive explicit lower and upper bounds for the Markov constant cn(λ), which are valid for all n and λ.