Abstract
Our main purpose is to describe necessary and sufficient conditions for the solvability of the ∂̄ -problem for biregular complex Clifford algebra valued functions of two higher dimensional variables in even dimensional Euclidean spaces. Since the biregular function theory falls naturally from the so-called isotonic Clifford analysis, the main idea of the proof is based on the notion of biregular-conjugate harmonic functions to be introduced here. Besides, whenever the ∂̄ -problem is solvable, we give the general solution of it in a quite explicit form.
Original language | English |
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Pages (from-to) | 579-586 |
Number of pages | 8 |
Journal | Archiv der Mathematik |
Volume | 97 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2011 |
Externally published | Yes |
Keywords
- Clifford analysis
- Conjugate harmonic functions
- ∂̄-problem