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REGULAR FUNCTIONS OF SEVERAL QUATERNIONIC VARIABLES AND THE CAUCHY--FUETER COMPLEX
 

Summary: REGULAR FUNCTIONS OF SEVERAL QUATERNIONIC VARIABLES
AND THE CAUCHY--FUETER COMPLEX
W.W. Adams (\Lambda) , C.A. Berenstein (\Lambda\Lambda) , P. Loustaunau (\Lambda\Lambda\Lambda) , I. Sabadini (y) , D.C. Struppa (\Lambda\Lambda\Lambda)
Abstract. We employ a classical idea of Ehrenpreis, together with a new algebraic
result, to give a new proof that regular functions of several quaternionic variables cannot
have compact singularities. As a byproduct we characterize those inhomogeneous Cauchy--
Fueter systems which admit solutions on convex sets. Our method readily extends to the
case of monogenic functions on Clifford Algebras. We finally study a free resolution of the
Cauchy--Fueter complex of differential operators and we obtain some new duality theorems
which hint at a hyperfunction theory of several quaternionic variables.
(*) Dept. of Mathematics, University of Maryland, College Park, MD 20742.
(**) Institute for Systems Research, University of Maryland, College Park, MD 20742.
(***) Dept. of Mathematical Sciences, George Mason University, Fairfax, VA 22030.
(y) Dept. of Mathematics, University of Milano, Milano, Italy.
This work was partially supported by NSF grants DMS9225043 and EEC9402384, and by
the Italian Ministry for the University (MURST).
1

1. Introduction
The well known Hartogs' theorem [7] shows that holomorphic functions in I

  

Source: Adams, William W. - Department of Mathematics, University of Maryland at College Park

 

Collections: Mathematics