Theory of Fundamental Bessel Functions of High Rank

2016/12/31 by Zhi Qi · 1 citation
Mathematics · #math.CA #msc:33E20 #msc:33E30 #msc:44A20

paper · pdf

published as Mem. Amer. Math. Soc., 267, no. 1303, vii+123 pp, 2020 · 126 pages. Remark 17.6 added for the $GL_2$ kernel formula. This is the combination of two papers "Theory of Fundamental Bessel Functions of High Rank - I: Fundamental Bessel Functions" [arXiv:1408.5652 ] and "II: Hankel Transforms and Fundamental Bessel Kernels" [arXiv:1411.6710]

arxiv created 2021/03/14 · arxiv updated 2021/03/16

Abstract

In this article, we shall study fundamental Bessel functions for GL_n(\mathbbF) arising from the Voronoï summation formula for any rank n and field \mathbbF = ℝ or ℂ, with focus on developing their analytic and asymptotic theory. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. We shall prove the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.

Citations

• Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions
• Theory of Bessel Functions of High Rank - II: Hankel Transforms and Fundamental Bessel Kernels

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