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

2012/04/16 by Fabrizio Colombo, José Óscar González-Cervantes, J. Oscar Gonzales-Cervantes +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic and Geometric Analysis #Basis (linear algebra) #Bergman kernel #Bergman space #Computer science #Function (biology) #Geometry #Holomorphic and Operator Theory #Mathematical analysis #Mathematics #Property (philosophy) #Pure mathematics #Quaternion #Space (punctuation) #math.CV

paper · pdf · doi:10.1080/17476933.2012.674521

published as Complex Variables and Elliptic Equations, 58 (2013), no. 10, 1355-1372

openalex publication_date 2012/04/16 · arxiv created 2014/06/21 · arxiv updated 2014/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This article has a twofold purpose: on one hand, we deepen the study of slice regular functions by studying their behaviour with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions 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.

Citations

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