Inequalities for Jacobi polynomials

TY - JOUR

T1 - Inequalities for Jacobi polynomials

AU - Haagerup, Uffe

AU - Schlichtkrull, Henrik

PY - 2014/2

Y1 - 2014/2

N2 - A Bernstein-type inequality is obtained for the Jacobi polynomials Pn(α,β)(x), which is uniform for all degrees n≥0, all real α,β≥0, and all values x ∈ [-1, 1]. It provides uniform bounds on a complete set of matrix coefficients for the irreducible representations of 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.

AB - A Bernstein-type inequality is obtained for the Jacobi polynomials Pn(α,β)(x), which is uniform for all degrees n≥0, all real α,β≥0, and all values x ∈ [-1, 1]. It provides uniform bounds on a complete set of matrix coefficients for the irreducible representations of 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.

U2 - 10.1007/s11139-013-9472-4

DO - 10.1007/s11139-013-9472-4

M3 - Journal article

SN - 1382-4090

VL - 33

SP - 227

EP - 246

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -