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arXiv · 1201.0495

Inequalities for Jacobi polynomials

Uffe Haagerup·Henrik Schlichtkrull
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Abstract

A Bernstein type inequality is obtained for the Jacobi polynomials $P_n^{α,β}(x)$, which is uniform for all degrees $n\ge0$, all real $α,β\ge0$, and all values $x\in [-1,1]$. It provides uniform bounds on a complete set of matrix coefficients for the irreducible representations of $\mathrm{SU}(2)$ with a decay of $d^{-1/4}$ in the dimension $d$ of the representation. Moreover it complements previous results of Krasikov on a conjecture of Erdélyi, Magnus and Nevai.

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BibTeXRIS

Uffe Haagerup, Henrik Schlichtkrull. 2012-01-30. Inequalities for Jacobi polynomials. https://arxiv.org/abs/1201.0495

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