# Some Open Problems on the Analysis of the Cauchy-Fueter System in Several Variables

## Document Type

Article

## Publication Date

1997

## Abstract

In the last few years there has been a resurgence of interest for the analysis of regular functions of a quaternionic variable and, more generally, for the analysis of monogenic functions of Clifford variables [28], of which quaternions are one of the simplest examples. There are many reasons for such a rebirth of a theory whose origin goes back to Fueter’s works in the first half of this century (actually, as Professor Shapiro pointed out [16], the first works in this direction are due to Moisil and Theodoresco [19], [20] $)$ . On one hand, Clifford analysis has acquired particular relevance in theoretical physics (see e.g. [5] $)$ , and, in particular, quaternionic quantum field theory is now being actively developed (see [5]); on the other hand, Clifford analysis has become increasily relevant to questions in classical harmonic analysis, as it has been clearly demonstratcd by thc work of McIntosh[18]$ (see also [28]) and more source of interest is the very recent novel approach due to Kravchenko and Shapiro, [16].

## Recommended Citation

Sabadini, I., & Struppa, D. C. (1997). Some open problems on the analysis of the Cauchy-Fueter system in several variables. *Suk. RIMS Kyoto Univ*, 1001, 1-21. Retrieved from http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1001-1.pdf

## Peer Reviewed

1

## Copyright

RIMS

## Comments

This article was originally published in

Suk. RIMS Kyoto Univ, volume 1001, in 1997.