Multivariate Bessel functions and multivariate Hankel transforms

TL;DR

This paper introduces a multivariate generalization of Bessel functions and extends the Hankel transform property to multiple dimensions, paralleling the Fourier transform's differentiation property.

Contribution

It provides a new multivariate Bessel function framework and extends the Hankel transform property to higher dimensions, advancing multivariate analysis techniques.

Findings

Multivariate Bessel functions are formally defined.

Hankel transform property is extended to multiple dimensions.

The framework parallels Fourier transform properties.

Abstract

The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel transform property is extended to many dimensions.