- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
17
2001
3
Morera type problems in Clifford analysis
Emilio
Marmolejo Olea
Universidad Nacional Autónoma de México, CUERNAVACA, MORELOS, MEXICO
The Pompeiu and the Morera problems have been stud ied in many contexts and generality . For example in di fferent spaces with diff erent groups locally without an invariant measure etc. The variations obtained exhibit the fascination of these problems . In this paper we present a new aspect: we study the case in which the functions have values over a Cli fford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Speci cally we show the equivalence between the Morera problem in Cli fford analysis and Pompeiu problem for surfaces in $\mathbb R^n$. We also show an invariance theorem. The non commutativity of the Cliff ord algebras brings in some peculiarities . Our main result is a theorem showing that the vanishing of the fi rst moments of a Cliff ord valued function implies Cli fford analyticity. The proof depends on results which show that a particular matrix system of convolution equations admits spectral synthesis .
General
559
585
10.4171/RMI/304
http://www.ems-ph.org/doi/10.4171/RMI/304