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arXiv · 1406.5586

The C-property for slice regular functions and applications to the Bergman space

Fabrizio Colombo·J. Oscar Gonzales-Cervantes
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Abstract

This paper has a twofold purpose: on one hand we deepen the study of slice regular functions by studying their behavior with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions $\mathbb{H}$ any slice regular function decomposes into the sum of four slice regular components each of them satisfying the C-property. Then, we will use these results to show a reproducing property of the Bergman kernels of the second kind.

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Fabrizio Colombo, J. Oscar Gonzales-Cervantes. 2014-06-21. The C-property for slice regular functions and applications to the Bergman space. https://doi.org/10.1080/17476933.2012.674521

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