Abstract
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.
To Nikolai Vasilevski on the occasion of his 60th birthdayframework of COFAA and SIP programs.
The first author was partially supported by CONACYT and by Instituto Politécnico Nacional as Doctoral scholarship and PIFI scholarship recipient.
The second and the third author were partially supported by CONACYT projects as well as by Instituto Politécnico Nacional in the
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Oscar González-Cervantes, J., Elena Luna-Elizarrarás, M., Shapiro, M. (2010). On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory. In: Duduchava, R., Gohberg, I., Grudsky, S.M., Rabinovich, V. (eds) Recent Trends in Toeplitz and Pseudodifferential Operators. Operator Theory: Advances and Applications, vol 210. Springer, Basel. https://doi.org/10.1007/978-3-0346-0548-9_5
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DOI: https://doi.org/10.1007/978-3-0346-0548-9_5
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