On the octonionic Bergman kernel
Jinxun Wang, Xingmin Li
TL;DR
This paper introduces a new inner product for octonionic Bergman spaces and explicitly derives the Bergman kernel within the complex framework of octonionic analysis, which is non-commutative and non-associative.
Contribution
It defines a novel inner product on octonionic Bergman spaces and explicitly computes the Bergman kernel in this non-associative setting.
Findings
Explicit form of the octonionic Bergman kernel derived
New inner product definition for octonionic Bergman space introduced
Framework applicable to non-commutative, non-associative analysis
Abstract
By introducing a suitable new definition for the inner product on the octonionic Bergman space, we determine the explicit form of the octonionic Bergman kernel, in the framework of octonionic analysis which is non-commutative and non-associative.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Holomorphic and Operator Theory · Sympathectomy and Hyperhidrosis Treatments