On the transformation formula of the slice Bergman kernels in the quaternion variables
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In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.
Abstract
In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.
참고문헌 (9)
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- F. Colombo, "On slice biregular functions and isomorphisms of Bergman spaces", Complex Var. Elliptic Equ, 57(7-8), pp.825~839 (2012)
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- G. Gentili, "A new theory of regular functions of a quaternionic vari-able", Adv. Math, 216(1), pp.279~301 (2007)
- S. G. Krantz, "Function theory of several complex variables" (2001), AMS Chelsea Publishing
- J.-D. Park, "On the zeros of the slice Bergman kernels for the upper half space and the unit ball on quaternions and Clifford algebras", Complex Analysis and Operator Theory