TY - JOUR
T1 - On the Bergman Theory for Solenoidal and Irrotational Vector Fields. II. Conformal Covariance and Invariance of the Main Objects
AU - González-Cervantes, J. Oscar
AU - Luna-Elizarrarás, M. E.
AU - Shapiro, M.
N1 - Funding Information:
J. O. González-Cervantes was partially supported by CONACYT and by Instituto Politécnico Nacional as Doctoral scholarship and PIFI scholarship recipient. M. E. Luna-Elizarrar and M. Shapiro were partially supported by CONACYT projects as well as by Instituto Politécnico Nacional in the framework of COFAA and SIP programs.
PY - 2011/3
Y1 - 2011/3
N2 - This is a continuation of our work (González-Cervantes et al. in On the Bergman theory for solenoidal and irrotational vector fields. I. General theory. Operator theory: advances and applications. Birkhauser, accepted) where for solenoidal and irrotational vector fields theory as well as for the Moisil-Théodoresco quaternionic analysis we introduced the notions of the Bergman space and the Bergman reproducing kernel and studied their main properties. In particular, we described the behavior of the Bergman theory for a given domain whenever the domain is transformed by a conformal map. The formulas obtained hint that the corresponding objects (spaces, operators, etc.) can be characterized as conformally covariant or invariant, and in the present paper we construct a series of categories and functors which allow us to give such characterizations in precise terms.
AB - This is a continuation of our work (González-Cervantes et al. in On the Bergman theory for solenoidal and irrotational vector fields. I. General theory. Operator theory: advances and applications. Birkhauser, accepted) where for solenoidal and irrotational vector fields theory as well as for the Moisil-Théodoresco quaternionic analysis we introduced the notions of the Bergman space and the Bergman reproducing kernel and studied their main properties. In particular, we described the behavior of the Bergman theory for a given domain whenever the domain is transformed by a conformal map. The formulas obtained hint that the corresponding objects (spaces, operators, etc.) can be characterized as conformally covariant or invariant, and in the present paper we construct a series of categories and functors which allow us to give such characterizations in precise terms.
KW - Categories and functors
KW - Hyperholomorphic Bergman spaces
KW - Quaternionic Möbius transformations
KW - Quaternionic analysis
KW - Vector fields
UR - http://www.scopus.com/inward/record.url?scp=79951950968&partnerID=8YFLogxK
U2 - 10.1007/s11785-009-0030-4
DO - 10.1007/s11785-009-0030-4
M3 - Artículo
SN - 1661-8254
VL - 5
SP - 237
EP - 251
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 1
ER -