On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory

  • José Oscar González-Cervantes
  • María Elena Luna-Elizarrarás
  • Michael Shapiro
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)


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. 


Vector fields quaternionic analysis hyperholomorphic Bergman spaces quaternionic Möbius transformations categories and functors 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • José Oscar González-Cervantes
    • 1
  • María Elena Luna-Elizarrarás
    • 1
  • Michael Shapiro
    • 1
  1. 1.Instituto Politécnico NacionalE.S.F.M.MexicoMexico

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