Advances in Applied Clifford Algebras

, Volume 17, Issue 3, pp 555–573 | Cite as

Semi-Harmonicity, Integral Means and Euler Type Vector Fields

  • Chia-chi Tung


The Dirichlet product of functions on a semi-Riemann domain and generalized Euler vector fields, which include the radial, \(\bar{\partial}\)-Euler, and the \(\bar{\partial}\)-Neumann vector fields, are introduced. The integral means and the harmonic residues of functions on a Riemann domain are studied. The notion of semi-harmonicity of functions on a complex space is introduced. It is shown that, on a Riemann domain, the semi-harmonicity of a locally integrable function is characterized by local mean-value properties as well as by weak harmonicity. In particular, the Weyl’s Lemma is extended to a Riemann domain.

Mathematics Subject Classification (2000).

Primary: 31C05 Secondary: 32C30, 31B10 


Semi-Riemann domain \(\bar{\partial}\)-Euler vector field \(\bar{\partial}\)-Neumann vector field semi-harmonicity weak harmonicity Dirichlet product 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Dept. of Mathematics and StatisticsMinnesota State University, MankatoMankatoUSA

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