On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory
For solenoidal and irrotational vector fields as well as for quaternionic analysis of the Moisil-Théodoresco operator we introduce the notions of the Bergman space and the Bergman reproducing kernel; main properties of them are studied. Among other objects of our interest are: the analogues of the Bergman projections; the behavior of the Bergman theory for a given domain whenever the domain is transformed by a conformal map.
Mathematics Subject Classification (2000)37C10 32A25 47B32 30G35.
KeywordsVector fields quaternionic analysis hyperholomorphic Bergman spaces quaternionic Möbius transformations categories and functors
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