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

TL;DR

This paper explores the analytic and representation-theoretic aspects of Hankel transforms and fundamental Bessel kernels of arbitrary rank over archimedean fields, extending the theoretical framework of Bessel functions.

Contribution

It provides a comprehensive analysis of high-rank Bessel functions, linking their analytic properties with representation theory over archimedean fields.

Findings

Develops a new representation-theoretic interpretation of Hankel transforms.

Extends the theory of Bessel functions to arbitrary rank.

Provides insights into the structure of fundamental Bessel kernels.

Abstract

In this article we shall study the analytic theory and the representation theoretic interpretations of Hankel transforms and fundamental Bessel kernels of an arbitrary rank over an archimedean field.