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Autumn 2017 A formulation of the Jacobi coefficients $c^l_j(\alpha, \beta)$ via Bell polynomials
Stuart Day, Ali Taheri
Adv. Oper. Theory 2(4): 506-515 (Autumn 2017). DOI: 10.22034/aot.1705-1163

Abstract

The Jacobi polynomials $(\mathscr{P}^{(\alpha, \beta)}_k: k \ge 0, \alpha, \beta >-1)$ are deeply intertwined with the Laplacian on compact rank one symmetric spaces. They represent the spherical or zonal functions and as such constitute the main ingredients in describing the spectral measures and spectral projections associated with the Laplacian on these spaces. In this note we strengthen this connection by showing that a set of spectral and geometric quantities associated with Jacobi operator fully describe the Maclaurin coefficients associated with the heat and other related Schwartzian kernels and present an explicit formulation of these quantities using the Bell polynomials.

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Stuart Day. Ali Taheri. "A formulation of the Jacobi coefficients $c^l_j(\alpha, \beta)$ via Bell polynomials." Adv. Oper. Theory 2 (4) 506 - 515, Autumn 2017. https://doi.org/10.22034/aot.1705-1163

Information

Received: 13 May 2017; Accepted: 28 July 2017; Published: Autumn 2017
First available in Project Euclid: 4 December 2017

zbMATH: 06804225
MathSciNet: MR3730044
Digital Object Identifier: 10.22034/aot.1705-1163

Subjects:
Primary: 47E05
Secondary: 33C05, 33C45, 35C05, 35C10, 47D06

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.2 • No. 4 • Autumn 2017
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