Abstract
A Bernstein-type inequality is obtained for the Jacobi polynomials \(P_{n}^{(\alpha,\beta)} (x)\), 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.
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Haagerup, U., Schlichtkrull, H. Inequalities for Jacobi polynomials. Ramanujan J 33, 227–246 (2014). https://doi.org/10.1007/s11139-013-9472-4
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DOI: https://doi.org/10.1007/s11139-013-9472-4