• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1401-1409
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• 2016

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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1483-1490
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• 2018

In this note, it is proven that the slice Bergman kernels for some axially symmetric slice domains are zero-free by a simple method.