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Multivariate Bessel functions and multivariate Hankel transforms

Victor G. Zakharov

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.

Multivariate Bessel functions and multivariate Hankel transforms

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.

Paper Structure

This paper contains 7 sections, 3 theorems, 28 equations.

Table of Contents

  1. Abstract
  2. Introduction
  3. Proof
  4. Multidimensional Hankel transform
  5. One-dimensional Hankel Transform
  6. $n$-dimensional Hankel transform
  7. Future trends

Key Result

Theorem 1

Two-dimensional Bessel function Jab is a solution of two-dimensional Bessel differential equation 2DBE.

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Remark 1
  • Lemma 1
  • proof
  • Remark 2
  • Theorem 2