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INICIO | 19 de mayo de 2024
  

Morera type problems in Clifford analysis.

Título inglés Morera type problems in Clifford analysis.
Título español Problemas de tipo Morera en análisis de Clifford.
Autor/es Marmolejo Olea, Emilio
Organización Inst. Mat. Unid. Cuernavaca UNAM, Cuernavaca, Méjico
Revista 0213-2230
Publicación 2001, 17 (3): 559-585, 31 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different 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 Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Specifically, we show the equivalence between the Morera problem in Clifford analysis and Pompeiu problem for surfaces in Rn. We also show an invariance theorem. The non-commutativity of the Clifford algebras brings in some peculiarities.
Our main result is a theorem showing that the vanishing of the first moments of a Clifford valued function implies Clifford analyticity. The proof depends on results which show that a particular matrix system of convolution equations admits spectral synthesis.
Clasificación UNESCO 120213
Palabras clave español Álgebras de Clifford ; Convolución ; Funciones de Bessel
Código MathReviews MR1900895
Código Z-Math Zbl 1058.30051
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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