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| Softcover ISBN: | 978-1-4704-4325-2 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 267; 2020; 123 pp
In this article, the author studies fundamental Bessel functions for \(\mathrm{GL}_n(\mathbb F)\) arising from the Voronoí summation formula for any rank \(n\) and field \(\mathbb F = \mathbb R\) or \(\mathbb C\), with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
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Table of Contents
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Chapters
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Introduction
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1. Hankel Transforms and Bessel Kernels
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2. Analytic Theory of Bessel Functions
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3. Bessel Kernels
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4. Hankel Transforms and Bessel Kernels in Representation Theory
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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In this article, the author studies fundamental Bessel functions for \(\mathrm{GL}_n(\mathbb F)\) arising from the Voronoí summation formula for any rank \(n\) and field \(\mathbb F = \mathbb R\) or \(\mathbb C\), with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
-
Chapters
-
Introduction
-
1. Hankel Transforms and Bessel Kernels
-
2. Analytic Theory of Bessel Functions
-
3. Bessel Kernels
-
4. Hankel Transforms and Bessel Kernels in Representation Theory
