### Abstract

Original language | American English |
---|---|

Pages (from-to) | 237-251 |

Number of pages | 211 |

Journal | Complex Analysis and Operator Theory |

DOIs | |

State | Published - 1 Mar 2011 |

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**On the Bergman Theory for Solenoidal and Irrotational Vector Fields. II. Conformal Covariance and Invariance of the Main Objects.** / González-Cervantes, J. Oscar; Luna-Elizarrarás, M. E.; Shapiro, M.

Research output: Contribution to journal › Article › Research › peer-review

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.

PY - 2011/3/1

Y1 - 2011/3/1

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. © 2009 Birkhäuser Verlag Basel/Switzerland.

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. © 2009 Birkhäuser Verlag Basel/Switzerland.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79951950968&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=79951950968&origin=inward

U2 - 10.1007/s11785-009-0030-4

DO - 10.1007/s11785-009-0030-4

M3 - Article

SP - 237

EP - 251

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

SN - 1661-8254

ER -